Which slot is the one that still works? I may guess it's number one (the top leftmost viewed from behind).
Did the problem happen suddently or did it begin as a single (or double: #2 and #4) slot malfunction and lately the third one (say #3) stopped working?
Chances are you have contact problems between the I/O Port Block and the Keyboard PCB (loosen screws prone to this behavior), nevertheless this usually causes the slots to stop working in pairs as slots 1 & 3 are internally wired toghether and slots 2 & 4 also are.
This should explain the problem with the pair of non working slots.
For the remaining faulty slot you might have a problem in the above mentioned internal wiring, or some dirtiness (e.g.: battery corrosion) that avoid proper contact or, in the worst case, a broken path inside the block.
Wichever the case you'd better try this first:
Twist both HP41's ends (you can't harm your calc unless you apply a *really* excesive force) this will make the contacts to sligthly move so it can displace some minor rust.
Should it becomes ineffective, try to press both halves of yuor 41, while a module is connected in one of the non working slots, and check if it's recognized.
Those are only diagnostics steps, anyway you should have to open your calc and make a contact cleaning, both on the Keyboard PCB and the I/O Port Block. Iso Propylic Alcohol is suitable for the task, if there is "greenish/blue" battery corrosion traces, a diluted acid like Acetic (vinegar) or Citric (lemon) will fit the needs, clean again with IPA once the acid cleaning is done.
Cotton tipped sticks are great for the job. Care should be taken to avoid IPA or acid reaching the display area. After that make sure to dry the whole thing completely.
If one or more wiring paths are broken... Well, if you are happy (like I am) with a soldering iron in your hands, then you know what to do, otherwise, you're more likely to avoid trying and messing it all up with.
Be careful when screwing it back as plastic poles tends to broke, keep both halves tightly toghether with your hand while screwing and do not overscrew, just set them firmly.
I'd enjoy doing the task for you but I'm really far away from the rest of the world :-)
Regards from the Canary Islands.
(Pls, excuse my English)