...you might try other options before replacing it..

1. If you have a different power cord to try, simply swap in another known "good" power cord and see if it makes a difference..

2. Because power strips can occasionally cause issues, try plugging straight into the wall socket.

3. As to your statement: "would not turn on at all"....what EXACTLY does that mean? Although you see the green light on the back of the tower, do you hear fans turning inside? Do you hear the hard drive spin up at all? If none of that is occurring, and none of the steps above help, then your next step is to replace the power supply.. If you're unable to accomplish the task, then a qualified tech at a local shop should be able to do it easily and quickly...

A quick internet search should give you instructions for performing the power supply replacement, if you're feeling adventurous. Making sure it's the right size is important, (ATX vs something else), and for many, simply marking each of the current connection wires with masking tape/numbers should allow you to correctly connect all the new wiring when you replace the unit... It's up to you.

Hope this helps.