Got it! I had the host that the server resided on. I was able to update the connection string to the following:
my $dbh=DBI->connect("DBI:Sybase:host=<hostname>;port=2832",$user,$password);
Since the hostname didn't have a slash in it, I was able to use the port that the server was using. I was able to connect so that I can continue testing.
I appreciated the comments!