Be careful with contact cleaner. The cleaner should be applied sparingly to the contact terminals on rotary switches. Contact cleaner should never be sprayed on the entire rotary switch.
The LR-5555 and 5555A used the ALPS AC power switch which is mounted on the rear of the Speaker Mode/power switch. The ALPS switch is notorious for failing. The spring switch contacts in the ALPS housing, after numerous ON/OFF AC hot switching are probably pretty well burnt into almost non-existence. Sometimes you can remove the switch, disassemble it, clean/burnish the contacts, and maybe get a little more use out of it. The receiver and switch are probably close to 50 years old. Unfortunately, the ALPS switch hasn't been manufactured in many years. I sold my last ALPS switch in my inventory probably close 20 years ago. If you're good at metal fabrication and have access to spring metal, You can probably fabricate a new set of internal contacts for the ALPS switch.
Now, you can leave the LR-5555A power switch in the A, B, C speaker position all the time and plug the LR-5555A into a switched power strip. On the power strip, flip the switch on the power strip to ON to turn on the receiver.
For FM or FM stereo reception, make sure you have some sort of "FM antenna" or some length of wire attached to the FM antenna terminal on the back. AM uses the loopstick antenna that's hanging off the back of the receiver.
Of course, the LR-5555A could have other problems. difficult to tell from your description.