Just figured I'd post this since I ended up sandwiched between two posts asking for pretty much a "free full version" of this game. Interestingly enough, there is a full version that is both free, and comes straight from the company itself, so no illegal activity necessary.
PRESIDENT FOREVER 2004
I just downloaded it, and it's no P4E16/PI, but it's a good enough taste. It comes with four scenarios, 2004, 1992, 1980, and 1960. There doesn't seem to be any primaries, but some people have made scenarios where you can just play the primary. In that sense, it's much more limited, but there's nothing stopping you from added candidates, and the game even comes with a candidate editor.
Sure, it's over 10 years old, but it's not awful and it seems to run fine on Windows 10.
There are a lot of custom scenarios available, though some download links may not work. Looking through the scenario names, it can be modified in pretty much the same way the current games can, to include foreign, fictional, and even state/city level campaigns.
So, if you can't afford the latest game or aren't sure you want to buy the most recent incarnation or you just like free things, here's an alternative. Go download it, play it, then flood the thread with screenshots like the rest of us.