Your computer is VERY susceptible to interference. Every single doodad sticking up on your soundcard acts like an antenna. The design of the card is VERY important in eliminating as much noise as possible.
A cheap soundcard like you have will typically have -40db of noise. A slightly better designed card, for about the same price, will give you a noise floor at about -70db. (the Ensoniq AudioPCI retails for $30)
Things you should do:
1) Disable ALL recording and playback sources that you're not using. You should only have enabled Line In on the recording control, and Master Volume, Wave Volume, and perhaps MIDI/Synth Volume on the playback control. I've found that simply muting CD Audio can decrease noise considerably.
2) Unplug ANYTHING running into or coming out of the soundcard and check your noise level once again. Bad PC speakers can do funky things for instance.
3) Turn the monitor off and see what happens....oh that won't work because you can't see what happens
You might have to listen...or just move the monitor around. Your monitor should be thought of as a big hunk of radio-active waste in that you should try your hardest to avoid it when recording....that is, get away from it and make sure it's not mucking with anything running into the soundcard.
Did you have anything plugged in when you were moving your computer around?
My guess with the info you've given is that when you're moving your computer, it's like moving a big clunky antenna. That's why your noise is jumping around.
You mentioned that it's picking up your voice? Is this true or are you just relating that ugly noise floor to the sounds of your room?
Slackmaster 2000