Hey ausdb, welcome to cofffeesnobs :)
Remember, there are no stupid questions, only stupid people (only kidding) ;)
Sounds to me as though three-way valve - that opens to release pressure in the grouphead after you pour a shot - is stuck open. This can happen if the machine isnt backflushed regularly, as coffee oils gradually build up over time. It could also be that the pressure gauge has stopped working (this is a known fault), but if the former is the case it would be hard to tell.
When you use a fine grind and tamp hard to the point that no coffee comes through, does the pump make a low, laboring noise? This is what youd expect if it was working correctly.
Water should only flow into drip tray *after* you have ended the shot, not during. The fact that you can totally block the flow of water through the group without the pressure needle moving also makes me think that the three-way is stuck open.
Backflushing with either a cleaning tablet or commercial espresso machine cleaner (which is much cheaper) should do the trick if Im right about the three-way valve. The manual has instructions on how to run the automatic cleaning program, but Id be inclined to use the manual button instead to get some dissolved cleaner and water into the pressure release pipe, then stop the machine and leave it to sit for ten-15 minutes. Repeat with the cleaner, then a few times with plain water to rinse and with any luck you should be in business.