I'm relatively new to posting on this board, so I hope that I'm at all beneficial.
There are a few questions I have, forgive me if you've already covered it and I missed it. From what I'm gathering, if you just turn your computer on and leave it alone, the screen turns off in 5-7 seconds. However, you apparently are able to keep it on longer if you are able to get into WinXP CD repair. Forgive me for saying this since I mean no offense, but I'm also assuming that since you're 15, you probably have a few basic things to learn about troubleshooting computers.
The question I had, is when you say you hear the sound of your computer starting up, do you mean the startup music of Windows, or just ticks and beeps from your computer?
If it's just clicks and beeps from your computer, the first thing I would check to see is if your two hard drives are setup correctly on MASTER/SLAVE (you have a 40 GB and a 20 GB?). You may have just gotten the hard drives mixed around. The hard drive that has Windows on it usually should be on the MASTER setting and should be in the middle port on your IDE ribbon. The other should be on the SLAVE setting and on the end of the ribbon. The ribbon for the hard drives is usually IDE1 on the motherboard.
If you actually are able to hear the Windows music and whatever that indicates that Windows has started up and it's blank, the first thing I would check then, is if you are able to get into safe mode without the monitor going blank. To do this, when you're computer is starting up, continually tap on the F8 key until a menu comes up. In the menu will be an option to get into safe mode.
If you can get into safe mode without any problems, that indicates to me that it's a driver problem or video card setting. You'll want to see if Windows is still trying to use the "new" video card or any of it's software even though it's no longer installed. Go into CONTROL PANEL -> SYSTEM -> HARDWARE -> DEVICE MANAGER. Is there a "!" under "Display adapters" or is the "new" video card still listed? If so, disable the "new" video card &/or reinstall the one you're using, whichever is appropriate. Also, go into CONTROL PANEL -> DISPLAY -> SETTINGS. Some of the new video cards have multiple displays. Make sure you're using your monitor as the "primary" display.
Unfortunately, if you can't get into safe mode without the monitor going blank, I'm running out of options. I would try to reinstall Windows from scratch (make sure you delete and create the partition, and don't just overwrite Windows) and hopefully that would work. I would certainly troubleshoot this more before saying that it's "hardware gone bad", unless of course, it's obvious. I would definitely check to see if your dad's monitor works, and I would tell him with all confidence that his monitor is in no danger or risk of being ruined just from trying it on your computer.
Well, I hope something I said helps in fixing your problem. I'll be back to check. Certainly, if you get further or find a solution, please post back here to let us all know.