Hi.
As others have said, a 12-year-old machine has done well. I'll be blunt; it's not worth fixing. Your best bet is to extract the hard drive and fit it into either an external case, or a spare bay on a second computer to extract the data.
The biggest issue you will face the issue that the drive is almost certainly a PATA/IDE style, which uses different connectors and cables from the current standard of SATA.
If you do want to fix it, then a good start point is this:
https://www.manualslib.com/manual/681188/Dell-Dimension-5000.html?page=8
Back in the day, computer designers would put in 'beep codes' that help diagnose problems at startup.
When you switch it on, does it beep at you? If it does, those beeps are telling you someting. The link above tells you the beep codes for a Dell Dimension 5000 series.
It might narrow the problem down to memory, or disk or motherboard, or something else.
If that dos not work, you can buy external disk cases for a PATA/IDE drive. You'll need to remove the drive from the machine (easy task - just needs scredrivers and a steady hand) and replace it into the external caddy then plug it in to a new computer with the USB cable provided.
Good luck!