My monitor is 8 years old. Now when I turn my system on the power light on the monitor flashes for some time and then the monitor will kick in, and I get a picture and the button stops flashing. But, if I let it rest it does this all over again. Is this an old monitor or a computer problem? When I had it diagnosed they didn't find any problems in my computer parts. Can you help?
Sounds like your system has gone to sleep cutting off the display signal to your monitor. Nothing unusual here. If you provide your Operating System I will update my answer to include stopping your system going to sleep, although there really isn't anything to worry about.
I say this taking into account your monitor is 8 years old and likely similar to one I used to have. If, however, this behavior is somehow new do update your question taking this into account and an answer can be researched.