All I can do is ping...

Dear gurus,

I have a RedHat 7.1 server that is (kind of) attacked by spammers. The
problem is that the spammer uses my domain name to send out his crap.
I don't have an open relay. The spam is not sent via my box, but I got
all the bounces. The server is running Postfix 2.14 and I had to turn
logging of because I get approx 200 MB log in every 24 hours.

The problem is that my old PII can't stand the it. It is going down.
All of a sudden I'm unable to login. The server doesn't respond to
anything except ping. I do have enough disk space.

The question is how I can track down the problem. I can't stop the
spammer but I want to improve the uptime on my RedHat box. Please give
me some advice.

TIA,
/David