Supershandy,could be your lasers on its way out or you may be lucky and it just needs a clean.If after cleaning it don't work either buy a laser or a new drive and flash your fw over to the new drive.Give flashing it a try and see what happens,you can always put it back to stock.
If you got downloaded content on your hdd then you can play it from your hdd,but if you copy an orig game to hdd,you need the disc in the drive to play it from hdd becaue as said it does make checks during the start of the game and within the game,it just loads slightly quicker and saves your drive if you play from the hdd.
off topic but.. I got the 120gb version of this for my slim:
60GB Hard Drive HDD for Xbox 360 Slim - Fast Speed 7200RPM - $29.75 - JacobsParts Inc
all they have lefty for the high speed is the 60gb but its a freakin steal at that price and its FAST!