Ok, so this gal is not as helpless as she thought
Taking apart the computer casing was simple enough but boy was it dirty in there! I suppose that's what having five cats will do!
So yeah, through trial and error, I isolated the problem to the power supply unit (PSU) Go me! I found a website which had pictures for my unit and gave step by step instructions on how to replace it.
Ordered a new one off the web and receieved it yesterday. The hardest part was getting into the small space under the floppy drive to remove the connection to the CPU and replace it. (that made me nervous as heck and now my fingers hurt!) Some he-man must have put those connectors in. They were tight!
Took one connection out at a time, matched it up with the new PSU connectors and plugged them in as I went along. Easy. Next thing I knew I was ready to to turn it on. Guess what? *dances* Everything worked perfectly. Even the floppy drive which had gone south about a year ago works now.
Thanks to you all for your help! You gave me the confidence to do it on my own.