Since you indicate that you tried with Apache::DBI, I'm guessing you're running this on mod_perl.

If so, Apache might just be spawning a LOT of clients to deal with your requests. I think the easiest solution is to place a frontend proxy-only Apache, hide your mod_perl Apache from users, and set MaxClients to some low value that your database can withstand safely

Of course, I don't know the entire picture, so I may be way off...