I take it that with it being 10 years old, it must have, at the best, Windows XP installed as an operating system. Let us know if it is any different.
To compare before and after times, shut down the computer and restart it, time how long it takes to boot up to ready to use.
Firstly, open your antivirus program and update it then run a full scan. Let it quarantine anything it finds.
Next, open which ever antispyware/antimalware you have and update that, then run a full scan. Let it quarantine anything it finds.
Next, do as Rich says and install Ccleaner, instructions
HERE but ignore the bits about the registry cleaner for now. Just run the Cleaner.
Next, install a defragmenter from the list at the top of the Computer Threads, Defraggler will do, and run it.
Next use the Ccleaner Startup list to disable any programs that you do not use daily. Any you are not sure of, leave enabled for now.
If there are more than about six items, make a list and post it back here.
Shut down and then reboot and time it again, compare the time.
dave