I also have an '01 GS and I do not have this problem.
Though when I checked compression, the cylinder that still had the spark plug in it, I kept the plug wire connected, while the cylinder I was testing I had the plug wire on the grounding post.
Make sure that your DESS key hasn't been pluged in for more then 10 minutes, as per the operators manual after 10 minutes the key has to be pulled and reinserted in order to start.
Also make sure that the plug going into the top of the rear electrical box is pluged in. I found out if that isn't plugged in your entire starting/ignition system is dead.
-TheChad