Checking if computer is compromised?
Solution 1:
Use a network sniffer like Wireshark to see what kind of traffic is send over your network interface?
Solution 2:
$ sudo apt-get install htop
It's a cooler version of 'top' so you can go through all the processes. Check them all out, see if you see one in particular that is running which you didn't expect.
Check your crontab. Check "ps waux | less".
Next: download rootkit scanners, make sure you didn't get, in the parlance, pwned.