I was planning on running a x7200 desktop replacement with an i7-960 and 2x 6990m's in CF.
I'm not looking to make a fortune out of this like some people, but I won't be on my computer for about 22 hours a day, so I figured I could put it to work.
Bitcoin doesn't need much bandwidth but it does need a stable connection. It should work over dial up or satellite connections although you might get some more stales due to latency.
Is the computer really yours? If you are planning to run this stuff on an army computer they might not be too happy about it. They will notice the network traffic if they take half a glance at a network dump.