There are a myriad of reasons why your system is slow such as driver conflicts or driver corruption, infections, heat issues, software conflicts, etc. Have you attempted to boot into Safe Mode and try to scan for infections?
Another standard diagnostic step is as parsalian points out is to do a harddrive diagnostics. Your HD manufacturer will supply a free utility that you run from your PC. Seagates Sea Tools will work with many brands.
Launch EventVwr.msc from a Run box; or open “Administrative Tools” in the Control Panel then launch Event Viewer. Tell us if there are any Red Xs or Yellow Triangles and where.
Again, from the Run Box type in ChkDsk and hit Okay. On step 2 tell us if it says "recovering lost files."
Did you have this problem prior to your external drive? You said you removed, how? Physically or did it come with any software? Lexluethar hunch may be the right one.
Here are the steps to memtest and you have already done a few (I was tired of constantly typing them out so I made a template!
1. Go to Memtest86+ - Advanced Memory Diagnostic Tool
and download the latest ISO version. It is free and perfectly safe.
2. Burn to a CD.
3. Place CD in your drive and reboot with CD in drive. The test will take over. For some people the CD/DVD ROM drive must be placed as First Bootable in the BIOS.
4. Let it run for a LONG time. The rule is a minimum of 7 Passes. There are 8 individual tests per Pass. Many people will start this test before going to bed and check it the next day.
5. If you have errors you have corrupted memory and it needs to be replaced.
6. Also, with errors you need to run this test per stick of RAM. Take out one and run the test. Then take that one out and put the other in and run the test.
* If you get errors let us know. Another thing you can do is run your system with only one stick and see if the issues continue; switch out the sticks and see what happens.