It looks to me like the problem with your code is it's missing a trailing pipe. If I use:

   my $cmd="ps -ef |grep -v grep |grep `cat /var/run/syslogd.pid` |"
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it works.

A smarter solution would make sure that the PID running was actually syslog, in case syslogd died and another process started with the same PID:

   my $cmd = "ps -ef |grep -v grep |grep `cat /var/run/syslogd.pid` 
                     |grep syslogd |"
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One of the modules that acts as a frontend to ps is what you really want, though (see the other responses).