Here's a few random things to do There are various more or less cryptic logs in /var/log.
You could boot off a Trisquel live CD or USB and leave the memory checker running overnight.
You could try making a live CD on another well behaving system and then running it on this system, first without the wifi and then with.
There are also packages rkhunter and chkrootkit, take their results with a grain of salt though.
