The specification of the new computer. Your f1graphics.cfg might have worked well with your old machine, but there could be a setting in there that the new machine doesn't like.
Take a look at it - the first line:
1 ; f1graphics.cfg controls all settings (default 0)
If yours says 1, you could turn it off by changing it to 0, which means ignore this file. (You can always put it back to 1 later if it doesn't help).
Now the game will decide what graphics settings to use instead. See if it solves the problem. If it does, you know there's something in there that needs tweaking.
If it doesn't, you could try taking a look at the Use CPU option in GPxPatch (GPxPatch tab). I always use the 0 option (which means use all CPU cores), but some say it should be set to 1 because anything else can cause problems on some computers. Again, just give it a try. It might help.
Then, assuming you're running the vanilla game (ie you haven't installed any mods) and it's still crashing you could try re-installing the game, just in case there are some corrupted files.
Also, as I mentioned before, enable debug in GPxPatch. That can often highlight a problem if there is one and save a lot of digging around. Random crashes can be quite difficult to pin down.