I really have difficulty imagining a situation in which Virginia stays loyal; even many of the nominal "Unionists" at the secession convention were opposed to allowing Lincoln to suppress the rebellion (which is why they seceded as soon as he made clear that he was calling up troops to do so). About the only approach that might work would be something a la the situation in Missouri, where local Unionist militias basically staged a coup against the secessionist governor, but I can't imagine there are enough pre-existing Unionist forces already in Virginia to pull off such a thing.
Nor can Virginia exactly bar federal troops, seeing as how there are already federal military institutions in the state (most prominently the arsenal at Harper's Ferry and the naval yard at Norfolk).
That said, assuming that these barriers are somehow overcome, Virginia staying unionist almost certainly sees North Carolina and Tennessee staying loyal (I don't know enough about the Arkansas secession movement to make a judgement on that case, but Arkansas is comparatively inconsequential anyway).
Robert E. Lee will not become overall Union commander (that position will stay with Scott, and then probably shift to another Northerner if he is replaced as OTL) but he likely will get some reasonably prominent command. I doubt he parlays it into a post-war political career, as he doesn't seem to have been particularly interested in one OTL, and he certainly seems unlikely to join the Republican Party (who will probably still dominate presidential elections post-war as OTL).
The South is vastly weaker, with its most populous states OTL now arrayed against it (and while there will probably be significant defections as with the OTL border states, most of the soldiers from these new border states will end up fighting for the Union ITTL), it's industry vastly weakened, it's position much less defensible (especially if they don't pull a Kentucky and thus allow Union troops to move through e.g. North Carolina). Nor should we forget that the vastly shorter coastline will make the blockade hit harder, faster.
But honestly, this probably means a much shorter war; slavery may or may not survive (I suspect that if we see a Reconstruction analog, the Reconstructed governments will abolish slavery during the period of Republican dominance, and revert to something resembling OTL Jim Crow once *Redemption gets underway).
However, as I said, I don't see a way to get Virginia to stay loyal without a POD so early that it will radically alter the contours of the Civil War as we know it.