in reply to concatenate/stitch multiple GZip fastq files and output combined gzip file

This:

while (<IN>) { while ( my $line = IN ) { print $outputfile $line ; } }
should be this:
while ( my $line = <IN> ) { print $outputfile $line ; }

But you should post the error you are getting here to give the Monks a chance to help without having to try to get your code to run.

The way forward always starts with a minimal test.