Try a couple of online portscans. Something like
www.cablemodemhelp.com/portscan.htm
There are more comprehensive ones around. The guy at grc.com might have a couple of things for that sort of thing.
If it's a Linux box, you should look at installing intrusion detection systems and blockers like PortSentry. I run a small (
www.netwinder.org) Linux firewall/router system at my flat and it works very nicely indeed. We set up an old P133 as a similar box last week in a couple of hours.
Things I use against av/hacks/spam/etc:
AV:
CAI's anti-virus stuff on all machines within the DMZ (I forget its actual name - EZArmour maybe)
Hacks:
A linux box running a recent kernel and ShoreWall as my gateway/DSL router (and the Linux machines in the network will only talk to members of the DMZ).
Spam:
SpamAssassin incorporating Razor (don't have the URLs to hand, but try spamassassin.org).