Desktop programs will not open vista/windows 7

So a few months ago, one of my Windows 7 computers started acting up. Whenever I downloaded a program, it would work for a few days/weeks. Then suddenly, it would randomly close and I would never be able to open it again. When I double click on a program, there is no reaction. I did notice, however, that the program appears in the Processes list in Task manager. Accepting defeat, I started using my other, older Vista computer. This computer has been working well for a few months and then started suffering from the same situation as the Windows 7 computer.

I'm extremely desperate and am willing to try anything.