When I go to shut my computer down, it just reboots.

Test your PSU or replace it if your power supply units fan is not working your PSU is faulty

One bad lead can cause a computer to continue on a cycle or to shutdown or fail to detect/ boot up a computer hard drive

Test all leads that attach to your hard drive including electrical extensions,IDE,SATA

the leads from your ((motherboard to your hard drive)) make sure they have a secure connection and are not faulty or just replace them there probably old and faulty
make sure all leads that are attached to your drives dvd\cd 3 1/2 inch floppy have secure connections and are not faulty even the electrical extensions or just replace them they are probably old and faulty a computer needs its connections to have an end so any faulty leads will end up with a computer error

hope this will help don