Using a ready-made solution from the BBTools / BBMap package (note, FastQC should provide these results as well):

reformat.sh in=file.fastq bhist=file.bhist.txt

As I am waiting for a drive scan (possible a catastrophic drive failure), why not unroll my own solution? Save the following as countG.pl:

#!/usr/bin/perl
while (<>){
  $lines++;
  if ( $lines % 4 == 2) {
    if ( /^G/i ) { $G++; }
    else { $H++; }
  }
}
print "Number of reads starting with G = $G\tNumber of reads starting with A/T/C/not-G = $H\n";

Make it executable with chmod +x countG.pl, and run it with ./countG.pl file.fastq, or zcat file.fastq.gz | ./countG.pl. Now, I only made this little script because I am waiting for the drive scan, please use reformat.sh for a more general and robust solution.