And having a full or nearly full hard disk doesn't slow down a computer. What slows it down is a lot of installed programs where many of them load these "quick start" things (essentially a large part of the program) into RAM at boot time. Each one takes up "just a little" RAM and processor time (they ping/"phone home" looking for updates), but they all add up into a mess. Even then, it's often just one, maybe two things sucking CPU cycles, and if they're at low priority it's not noticeable. But running out of RAM is Very Noticeable, as it starts to store parts of "RAM" on disk, and that's where things turn to molasses.
When suspecting something is wrong I run Task MAnager (ctrl-alt-delete), enable the CPU Time column and look to see what memory is left. I've mainly had problems when using the Windows search tool, especially when searching for "A word or phrase in the file." Dunno how Microsoft screwed that one up, the command-line utilities for MSDOS and *nix work just fine.