If you're going to go the usual portscan, service vulnerability probe, and service exploitation route, then using nessus would make your life much easier.
You may have to read some documentation to get it working if you're not familiar with setting up both server and client sides of a program on the same machine, but it's pretty easy and will tell you all the known vulnerabilities of the services your other machine is running.
You can also look at sites like milworm, securityfocus, packetstormsecurity, and others to get more information on service vulnerabilities or exploitation.
Are you the only user? If not, sniff the LAN traffic with a tool like wireshark to pick up web logins of the other users. Chances are they'll reuse them for their personal passwords on your other machine.