Trojan and Spyware Removal needed

my computer has been acting very weird lately, and I can't seem to figure out why, its randomly restarting, and trojan and virus scans have shown many infections which I would like to rid my computer off, and one of the scans revealed a "backdoor.irclogger" or something or other and its description was "to allow remote access to computer giving attackers direct access" which makes me a little insecure.

so if anyone could reccommend a free trojan and spyware removal program that would help me out, because i am young and short on cash to pay for a nice program that pctools suggests =P

and one more question,
is the random restarts a result of the trojans or is that a bigger problem?
any help will be greatly appreciated thanks.