Check if the trough has divots in it preventing balls from rolling to the end.

Even if the diverter is working, check if it needs to be adjusted. Make sure the diverter arm it has full range of movement and that it will, when fully activated, actually divert the ball to the popper as it should. I've seen some work themselves loose so even if the diverter coil is working, the diverter doesn't sit in the proper orientation to divert the ball.

Go into coil test one back and remove the balls with the program.
Go into switch test and drop the balls in one at a time to see if they all register in the trough.
If they do exit test and start game, if they don't then reseat the connectors on the trough boards and repeat test.
On game start it should load two balls into the VUKs off of the subway and stage the third one in the shooter lane.
If it keeps trying to load balls then you have a bad opto or a stuck/broken diverter in the subway.
Also check the switch in the shooter lane, if it is out of adjustment or bad the game will keep trying to stage a ball.

Copied this from an old thread on this subject. I had the same problem a while ago.

If this does not work google search STTNG pinball Balls keep loading. There are several old posts on this very subject. I believe I ended up replacing a board under the play field to stop my issue. Good hunting

CLEAN ALL OF THE OPTOS! Start there. The trough, all the subway optos, All of the optos for the 3 VUK and the optos for the cannons. Q-tip and alcohol. remove the screw holding the bracket or the board itself and rub them clean.

If they are yellow like the amber they drilled into in Jurassic Park, replace the optos.

I would guess it would be the opto right before the diverter. Put game to switch test and use your phone on camera mode to see if the transmitter led is lighting up. Use an IR remote control to see if the receiver opto is seeing the signal.

I had to replace my subway since the last time it broke a huge chunk came out and it looked like a sketch epoxy repair. At any rate, the new one is in (with metal protectors to hopefully guard against subway breaking shenanigans in the future. Doing this required removing the diverters and one thing I noticed is the one that loads the right VUK (the one that is outside the subway when in its rest position) is somewhat fickle to adjust. I originally set it up to the original setting (or close to it) but the new subway required some adjustment to get mounted well and I think that might've been enough to cause some issues.

I've been carefully adjusting it and on this last attempt, so far, balls end up going to the right VUK and I don't get the forever loading issue.

Just something for folks to think about maybe - there isn't a ton available online for adjusting that though I found this pretty fantastic video on the subject:

I think I'm on the right path perhaps. I had to repair a broken resister on the trough IR board which may have been complicating things but I'm finding the main issue is still the diverter. The problem is the grub screws were originally screwed in so tight they left pretty noticeable indents on the shaft. This makes it problematic to make adjustments. When I get it dialied in, it seems to work for a while but I suspect it's slipping back into the indents since going back and adjusting it causes it to work again (for a while).

So I went ahead and ordered a new diverter, new grub screws (lots), and also some new sleeves as I didn't have any spares and was only able to merely clean the current shafts. The action is good though, all the optos are (now after fixing the trough) good. Really seems to be the darn diverter itself.

In fact I found the spot to place my cellphone under the playfield to record it (right on top of the speaker) and was able to see when things would start to go off. The diverter would engage but would end up catching the ball instead of actually diverting. So when it disengaged, the ball would fall to the left lane instead of the right.