I noticed that the monk said only FTP access was allowed. That is specifically why I said it could be done through a CGI script. Here's an example of what I meant.

#!/usr/local/bin/perl

use CGI;
my $cgi = new CGI;

print $cgi->header('text/plain');

my $source_dir = "/home/me/source";
my $lib_dir    = "/home/me/lib";

my $module = $cgi->param('module');

chdir($source_dir) or die "Can't chdir to $source_dir: $!\n";

system("/bin/gunzip $module.tar.gz") and die "Can't gunzip $module.tar
+.gz\n";
system("/bin/tar xf $module.tar") and die "Can't untar $module.tar\n";

chdir("$source_dir/$module") or die "Can't chdir to $source_dir/$modul
+e: $!\n";

system("/usr/local/bin/perl Makefile.PL PREFIX=$lib_dir")
  and die "Error running Makefile.PL\n";
system("/usr/bin/make") and die "Error executing make\n";
system("/usr/bin/make test") and die "Error executing make test\n";
system("/usr/bin/make install") and die "Error executing make install.
+\n";
[download]

So, all one has to do is upload this script, upload the .tar.gz file to the source directory, and hit the script from the browser with the name of the module in the module parameter. All possible simply with FTP and CGI.

Obviously, the script needs better error checking and reporting, and it should capture STDERR from the system calls and send it to the browser along with STDOUT. (Calling a single shell script to handle all the unpacking and building might be an improvement.) I've just written this as a quick hack to get the general idea across.

Update: Please see DrManhattan's important addendum below; using this script as is would be a huge security risk! An improved script would use taint-checking and restrict the module name to a limited set of characters.