I have a Fedora server hosted remotely and for the last couple of days simple processes seem to be causing the server to slow down incredibly. I am starting to feel that the RAM or the HD might have some problems. What free software can I use to test these?
A slowdown can't result from bad RAM. Nothing to test here in your case.
If you have a faulty disk, your kernel log will show it. Just issue a "dmesg", or dig into /var/log/
On another terminal, ask for informations every 5 minutes:
You can be even more sure by creating a big file from random datas, and check its checksum. It must be the same as the one from the datas.
If you have disks that support SMART:
Check the manpages for -d as it might be different if you use a raidcontroller. Smartctl can be found in the smartmontools package.
If you want to check your RAM you should boot from a livedisk and perform a memory check. On ubuntu live disk it is one of booting options.