The real question is, how do you finally end the Depression without getting America fully into war-production mode necessitated by the war? That's why it's hard to answer.
My bet is something along these lines: bigger or more rather different New Deal programs (example: no GI bill, but Federally Subsidized Education Grants for all) combined with the trade boons of being the only economy geared for trade once the war is over and / or Lend Lease on Steriods. Note that in neither case am I saying that US Gov't spending actually increases to OTL WWII levels, simply that the New Deal changes and refines itself in order to keep voters satisfied that at the very least the safety net will be strengthened and improved. This simply means that as the economy recovers (probably over a longer period, perhaps through the 1950s), the safety net will stick around.
This altered New deal would leave a profound mark on American politics: consider, for example, that the primary reason why health care became an employer-funded benefit was due to wage and salary freezes during WWII. Without those freezes, a Truman-esque National Health Insurance plan (probably along the lines of the current Swiss model) might emerge quite easily. More so, since Cold War antipathy with communism won't be as marked. I'd consider the general trajectory of this movement to follow something like this: moderate Republicans take office in either 1940 or 1944. They change some of the New Deal programs, but leave many in place (if it's Wilkie, he makes it more pro-business; if it's Taft, he leaves in place some social programs like housing, etc). Essentially, the most crisis-oreinted efforts, like the WPA, fade in favor of more welfare-state oriented institutions that will form the bedrock of a future economic system. This prompts a new Democratic administration (possibly headed by Truman himself) that formalizes such programs and introduces new ones.
Now, positing the economic development of this alternate America is not without pitfalls. First, a major variable is the state of international fianance, free trade, and trade governing bodies. No American particiaption means no Bretton Woods or GATT to replace it. Whatever the settlement -- whether there's really not much of one or if the Europeans make one of their own -- it probably means that the development of world trade is slowed, somewhat, but will ultimately happens as companies and countries look for new markets. Second, is whether Europe is decimated enough to need a Marshall Plan which it won't get. I leave that an open question, but I'd guess the alt war probably isn't significant enough to require it.
Next, consider the lack of the baby boomers. Without American participation in the war, there'll be no return of the GIs and thus no pronounced rise in the number of births. On the surface, this may seem like a bad thing: no baby boomers means fewer consumers, which is not a good thing in a consumer driven economy. However, since we all will lack a pleasant 1950s with stable growth and the emergence of suburbans to house these people, we avoid a few things: first, we avoid the sense of OTL 1950s, namely that things were chugging along pretty well. Hence, on the political stage while the lack of WWII means that you won't have a Truman trying and succeeding in integrating the armed forces, you won't have (white) middle class America luxuriating in the idea that all is good and well with the world, their years of sacrifice and shortfall long past them.
Let's take this idea further: without WWII, you probably lack a military - industrial complex. No vast warehouses in Arkansas filled with surplus pajamas. On the other hand, you lack the man impetus behind Eisenhower's Interstate Highway System -- to move the army around. Granted, it's a great public works program for our evolved New Dealers, so I'm not proposing no highway system, merely a different one. That may not be such a bad thing, considering that OTL Highways killed the railroads and most particularly mass transit and so helped to usher in suburbia. If American cities remain dependent on mass transit for longer, they remain denser and American political attitudes will reflect it. Without suburbs to which to flee, you will either see more wholesale population movements or political change. This too has an impact on civil rights / politics: there's no room for white flight, for one, but so too is there a different tolerance for rioting. Indeed, since the original Levittowns were originally intended to provide mass appeal because they were cheap (rather than becasue they offered a "better" lifestyle), American cities may resemble European ones (Paris), with the slums / lower class areas on their outer rings, rather than their inner cores. That too will change the nature of political strife: will suburban slums be as apt to witnessing the erosion of the family? A loaded question, to say the least, but certainly poor suburban ethinc enclaves will have a different dynamic than OTL's poor urban ethinc enclaves.
On a big picture, by the mid-1950s, I imagine Europe is stable enough that American businesses will make inroads, regardless of the state of trade agreements. If noting else, they'll set up European subsidiaries and benefit from the chance at rock bottom capital investments. They will have to compete for business perhaps more cut-throatly, but that might not be too bad. Here, the US has no moral highground as the leader of the free world to protect, afterall.
One question may be whether TTL will see the broad gains in producivity which has seen the American economy grow over much of the last half-century. Firstly, it may not seem them as soon. Secondly, the labor movement is bound to be much different TTL, with differeing struggles with communism and without WWII to halt labor action. Perhaps the US adopts a German-style labor system, with labor unions more linked to management and thus workers more productive. Education may not get the boon it got with the GI bill, but it will still be important. Infrastructure will get built, if only because the US gov't in the 1940s and 1950s will be looking for more Keynesian programs.
In contrast to previous posters, I do not think that such a US will be less anti-colonialism in regard to its attitudes toward the ageing / crumbling European (and perhaps Japanese) Empires. I think quite the opposite will be true, at least among Democratic Administrations; Republicans might well tolerate more out of isolationsim/realpolitick. Nevertheless, the primary question here is whether the USSR exists and whether they've expanded their influence enough that there's something of a Cold War. Here, though, that War would be between Europe -- Britain and France and perhaps reconstructed Germany -- trying to hold together against the Evil Eastern Empire. The US would probably only begin to take a stand if China fell to the Communists. Even then, the US might be neutral; indeed, I could well see it leading a TTL's Non-Aligned Movment--what could better resonate with "traditional American isolatinism"? Such a movement would probably mean partnership with many of the anti-colonial, quasi-communist regimes of the Third World. And the US would of course feel great sympathy with these Republicans fighting against Monarchic / Corporatist Empires, since of course the US was the first such country.
To sum up, I don't think it's true to say that a USA that never fought WWII (because WWII was a different war) will be worse, better, less well-off or better well-of economically, politically, or socially. Rather, as in all things AH, it will be different first and foremost. The trajectory of something as complicated as the Civil Rights Movement is bound to be different: it may start later, but it may finish sooner as well, given the different nature of TTL. It may be wider in scope as well. Probably the most certain thing is that the US will stay fairly unactive in terms of military power. It may well invade / police some Latin American states, but not with anything like the resolve or ideological meddling of TTL's Cold War.