I run an Apache web server, and I recently added some perl CGI scripts
to run a small, interactive part of my web site. My problem is that my
web server is an old computer that gets easily overworked. When more
than a few people access the CGI pages at the same time, the site
starts to noticably slow down. I spent some time trying to make the
perl scripts more efficient, but after that effort, I became convinced
that the script itself can't be made much faster. I then turned to the
Apache documentation to see if I could tweak it to run scripts faster,
but no luck. Any ideas for how to make perl scripts run faster on my
server? Thanks.

I'd need to see the scripts to see if I think there are any real
speedup opportunites in them.  Otherwise your best best is just to
look for standard system performance tuning stuff.  I assume you are
running linux if it is apache on a small server?

http://www.linuxforums.org/desktop/linux_performance_tuning.html

The reality is though that apache is expensive and perl is expensive. 
You probably just need more horesepower.  There is only so much
optimization that can be done.

I largely agree with frankcorrao-ga.

Then there's apache's mod_perl as a possibility.  http://perl.apache.org/

can some of these perl scripts be converted to php (fast-cgi) or to a
simple binary cgi executable?