You say you can run your locally installed perl normally outside of the webserver context. So you could check which libc.so it is using in this case:

$ ldd -s /home/rsch/bioinfo/.perl/bin/perl
[download]

In the output, you'll see a paragraph beginning with find object=libc.so.1. Something like this:

 find object=libc.so.1; required by /usr/local/bin/perl
    search path=/usr/local/lib  (RPATH from file /usr/local/bin/perl)
    trying path=/usr/local/lib/libc.so.1
    search path=/usr/lib  (default)
    trying path=/usr/lib/libc.so.1
        libc.so.1 =>     /usr/lib/libc.so.1
[download]

Or, with LD_LIBRARY_PATH set:

find object=libc.so.1; required by /usr/local/bin/perl
    search path=/opt/SUNWits/Graphics-sw/xil/lib:/usr/openwin/lib:/opt
+/SUNWits/Graphics-sw/xgl/lib:/usr/dt/lib:/usr/openwin/lib:/usr/local/
+lib:/usr/lib:/usr/ucblib  (LD_LIBRARY_PATH)
    trying path=/opt/SUNWits/Graphics-sw/xil/lib/libc.so.1
    trying path=/usr/openwin/lib/libc.so.1
    trying path=/opt/SUNWits/Graphics-sw/xgl/lib/libc.so.1
    trying path=/usr/dt/lib/libc.so.1
    trying path=/usr/openwin/lib/libc.so.1
    trying path=/usr/local/lib/libc.so.1
    trying path=/usr/lib/libc.so.1
        libc.so.1 =>     /usr/lib/libc.so.1
[download]

Essentially, this tells you that libc.so has been found in /usr/lib/ (in my case). You can then add that directory to the shared object search path LD_LIBRARY_PATH in your CGI environment, just like you're already setting PERL5LIB.

(Report back what you get from ldd, ldd -s and ldd -sv, in case this doesn't help...)