The clutch may be stuck to the pressure plate or the flywheel -- especially after sitting engaged for 42 years.
You need to check the clutch release linkage first. This car has a mechanical linkage. Make sure the linkage is set to give just a little free play (say 1/2 in or so) at the clutch pedal. If you can't set it properly, chances are there is some problem with the throwout bearing or clutch assembly, and you may as well prepare to do a clutch job.
Once the linkage is adjusted, suggest you do some testing with the engine off. Put the car in gear and release the clutch. Can you roll the car without the engine turning over? If not, the clutch is probably stuck.
If the clutch is stuck, try putting the car on the ground pointed down the road. With the engine off, put the car in first, push down on the clutch, take the brake off and hit the starter. The engine will start and the car will move forward. Hit the throttle and try to jerk the drivetrain to free the clutch. This will usually break it free.
Just FYI, I have started a number of cars that have sat for 30-40 years or more. I usually can get them to run, but eventually they ended up being dismantled and rebuilt. I found that rings stick, seals fail, valves stick, etc. or the engine was just terribly worn when it was parked (who would park a good running car? Can happen, but usually not). I suggest you prepare emotionally for having to do this to your Dad's Healey, this is a great car that should be on the road. But good luck, who knows, you may be able to get it going without major work needed. Just make sure it has oil pressure and sounds like it is getting lubrication. Stop immediately if you hear any knocking or it overheats.
Bill.