No signal to monitor after ~30 seconds.

The computer is an older discontinued Gateway dx4300-03 and this has been an ongoing problem for me for roughly 6 months. At first it started as an intermittent issue, I would be gaming (nothing all that gpu or cpu intensive) and my monitor would randomly show no signal after about 30 or so minutes of gaming and then my computer would freeze and would require a system restore upon reboot. Now, my pc will begin booting up and last maybe 10-40 seconds before showing no signal again and freezing. Also, note that in the past I have had issues with random colored lines and random letters/symbols across the entire screen which was simply resolved each time by a reboot and system restore. My initial thought is my video card as all issues have seemed to be with the display. I don't have access to another machine other than a laptop so I can't test any of the components out of my machine. I have tried unplugging it and draining the residual power in the system but to no avail. Any opinions/tips/or possible fixes are welcomed. Thank you in advance.