I don't think it's possible. I've taken many a machine apart. The cassette door tabs should be "locked" in by a metal spring tab. So once the machine is apart and upside down the metal tab is screwed ontop of the plastic tab on the door. If you managed to remove the door without breaking it....That's pretty amazing. It's really not that hard to fix. Just flip the 424 over and take out all the screws you see on the bottom. Then inside you'll see ribbon wires with connectors attached to the boards. Take these off (mark them or draw a diagram so you know where to put them back- there's not too many anyways) You may have to remove the tape transport to get to the cassette cover. I don't remember exactly how the inside is set up. Take the screw(s) off of the spring tab. Put the door back on, screw the tab back down and reconnect everything. The most important thing is to remember where everything goes. How I learned was: (Some people may be too scared to experiement like this , but anyway) I just take apart what you need to (take pics of everything in seqence if you have to) until you find the problem. Go back to the pics if you need to for reference. I don't have to take pics anymore. Not bragging, but I have great memory. This is my method and it works 98% of the time.
Aaron
