I have a compaq desk top(brand new in 2001) that has been upgraded with more memory about 3 years ago. Just recently I tried to boot up comuter and it is locked at the compaq logo screen and does not boot. Any suggestions or troubleshooting advice?

First I would try reseating the CMOS battery. It is found on the motherboard and looks like a big version of the kinds of batteries that are in watches and small electronic equipment. Should look something like this:

http://www.google.com/imgres?q=cmos+battery&um=1&hl=en&tbm=isch&tbnid=qPCjyyqYzrruGM:&imgrefurl=http://www.cybernetman.com/kb/index.cfm/fuseaction/home.viewArticles/articleId/15&docid=JNPpiRW-240CaM&w=374&h=374&ei=MKJ8To6hPIqlsAKK3Iwb&zoom=1&iact=hc&vpx=497&vpy=329&dur=767&hovh=225&hovw=225&tx=98&ty=127&page=1&tbnh=164&tbnw=167&start=0&ndsp=8&ved=1t:429,r:6,s:0&biw=1024&bih=674

Does the PC make any beeps or noises when attempting to boot? If so what kinds of sounds are they?

Check the CMOS battery and try booting in safe mode. The computer is 10 years old and at this age any and all components and software are suspect to cause failure. You should try to put the Hard drive in a different machine via a external enclosure and recover your data. At this point reload you OS with the drive back in your computer. If you are able to reload you are not so good to go. Remember that the end of life cycle will be approaching or past on most software and Operating systems that are 10 years old. It is time to get a new computer so that you can keep updated and protected. If a new computer is out of reach you could switch to a Linux distro like Linux Mint or Ubuntu. Both are supported with updates and operate on less resources than Widows and make excellent choices to keep older equipment running longer