Yay, finally EM questions. My specialty.
So since it makes noise, does the coil try to fire?
There should be a hairpin you can remove to tilt this unit downwards to inspect the back, make sure it is not missing any obvious springs or there is no visible failure with the mechanics in the back. You may need to adjust the springs, and I have done this many times to repair similar problems. I just stretch them and attach them lower down the line of the spring but they also sell replacements.
You can also sand down the contacts with a very fine grit piece of sandpaper (wipe down after with a dry cloth) and then a very light coating of teflon grease over the contacts to make sure that end of things is running good.
The other thing may be the coil sleeves that needs replacement. There will be two coils, one to advance and one to reset (go the other direction), the one you're having trouble with is the reset one and also make sure the arm in the back for this one moves smoothly. If you push in the coil plungers by hand with the machine off and release, does the unit step up and down? Keep in mind you'll need to do it kind of quickly to simulate the fast force of a coil or it won't be an accurate simulation of it working right.
If you find you have difficulty pushing it inwards, replace the coil sleeve.
If you find it has difficulty pulling back out once it's in, adjust/replace the corresponding spring on the back of the unit.
Also, does the rotating bakelite (brown) plate have a crack in it? That may be an issue down the road, if not already.