The underside of the metal tray ('caddy') that the disk is mounted on has two small 'nubs' at the front. These protrude just enough so that the caddy is held in place by the keyboard case, even when the screws are removed.
Once all three screws are removed, you should be able to pull the caddy/disk out if you put your fingers in the indent in the plastic and initially pull with enough force to get the nubs over the case. It 'clicks' out, and after that the caddy slides out easily the rest of the way, as long as you keep it level! You can easily feel the click once it releases. On my T4 the nubs hold the disk firmly in place, but this probably varies from one keyboard to the next, so presumably the amount of force needed to overcome them varies too. Once you have done it the first time, you will be fine in future!
There is enough slack in the cable to remove the assembly completely from the keyboard, but only by five inches or so. Internally the cable should be held in place by being looped around part of the case, which should prevent you from pulling it out too far, possibly breaking its connection to the main DM circuit board.
When you replace the assembly, it slides easily into the keyboard case for most of the way as long as you keep it level, then it just needs a final push to re-engage the nubs in the case and secure the unit in place. In fact, since I remove the disk regularly from my T4 to back it up on my laptop (much faster than USB Storage Mode!), I don't bother replacing the screws because the disk unit is held securely enough by the nubs alone. However if you gig with the keyboard or are regularly moving it around, it would be best to use the screws!
Even though it your hard disk is now working, I would say that it is definitely worth removing the HD assembly and checking that the cable is pushed fully home in the socket on the disk. There is a cut out in the metal at the back of the caddie for the cable. This reduces the strain on the disk socket and stops the cable from moving around when you slide the assembly back into the case, so make sure that the cable is located in this!
Regards
Ian