Assuming that the previous suggestions of modifying the line terminator (see $/) fix your immediate issue, there are some style issues you may consider. These are some generally regarded good practices which you are free to ignore at your discretion:

1. Starting each script and module with use strict;use warnings; can save you a bunch of headaches. The virtues of these pragmas have been extolled extensively on this site. For example, Use strict warnings and diagnostics or die.
2. You should consider using 3-argument open instead of 2. It allows for some more security against malicious people and messing stuff up. If your case, line 5 would be changed to

   open(plate_file,'<',$filename.".csv") or die "Can't open: $!";

   See open,perlopentut for some more details.

3. Rather than building your own paths, you might consider using File::Spec to do it for you, in a platform independent way.
4. In fact, rather than rolling your own CSV parser, consider using Text::CSV.
5. Regarding your second question, in list context a regular expression returns the captured expressions. So you could write something like:

   #!/usr/bin/perl 
   
   use strict;
   use warnings;
   my @data;
   while(<DATA>) {
       my @row = split /,/,(/(.*)\n?/)[0]; # <-- nice and clear, right?
       shift(@row);
       push(@data,@row);
   }
   print join "\n", @data;
   __DATA__
   1,2,3,4
   2,3,4,5
   3,4,5,6
   [download]

I could go on, but that should give you plenty to chew on.