The best solution in cases like this since your equipment has no more warranty, is one of two: If you don´t really know what you are doing, DON´T DO IT, this makes things worst, so take it to a technician, or to a friend who can test and repair for you. The worst thing is trying to fix things that aren´t really damaged. If you know what you are doing, let´s go:
The first thing is to open the computer and test essencial pieces, always being very careful with your equipment ( remember static electricity ).
01 - Begin by testing your power supply. If the power supply is faulty, the rest won´t work at all.
02 - If the power supply is good, you should test bios, motherboard and CPU. Make a bios reset, by taking out the battery and putting the jumper which control bios reset on the reset position, wait for about 30 seconds and then put it back.
03 - You could test the power supply in the other computer in order to see if it´s good, but beware ! If the power supply is faulty, it could damage your other computer, so, there´s a solution, that is locating the power supply wires which turns it on, so, you could turn on the power supply without a computer, and with a multimeter, testing the voltages. ( the contrary may work: If the power supply is not good, you could bring the other computer power supply and test on it ).
04 - The most precious thing: You could and should check if your data on HD is intact, by putting the hard disc on other computer and see if it works. It it works, you could use a software called Acronis True Image ( or similar ) and make an image of the whole disk just in case. With this image, you can transfer the content back to the HD or to a new HD ( if necessary, some power problems could cause HD failure, but many times we can retrieve the information ) without losing any data. This has helped me a lot. Even yesterday, I had a problem like yours that my windows 7 wouldn´t boot up, blue screen. I simply put the Acronis True Image disk on the drive, booted up by it, located the image file on an external hard disk and restored the whole partition in 10 minutes. So, in 10 minutes, my PC was back on business with no problem. I highy recommend creating images of your boot disks from time to time. HDs are very impredictable pieces.