Well, it's a compaq. Probably made for budget purposes, I'm assuming.
That's what I have been doing with my Asus, which was already made with gaming in mind. Even then, it has been very hard. The mobo isn't ideal, the case has horrible ventilation, and the power supply was originally really cheap.
And that was over 800 bucks.
If the compaq is too old, you'd probably need a new mobo for a new socket to fit a new processor so you could take advantage of a new gpu, with some new ram, new fans to cool it all down, and a new psu to power all of these. Shiz, I don't remember compaq making terribly good cases either. I know our old compaq doesn't, although yours is probably several steps above, since our old one was only 400 or 500 bucks.
Probably no.
But it would be nice to have a link to your model.