Low voltage in my light switch after relocating a ceiling box
Illuminated wall switch?  

OK, so this is a powered switch.

It requires power to do its "lighting up" thing.  

It could just be changed to a non-lighted switch, and some of these issues would "go away", but it would leave another dangling issue... plus, that's no fun :)

On classic devices like this, they do not have a separate neutral wire going to the switch.  They depend on being in series with an incandescent light.  Incandescents, which are off, are basically a dead short.  

When you changed this to a fan (you used a fan-rated box, right?) you now have the lighted switch in series with a fan remote control module. When the module is quiescent, it draws very little power, and the lamp inside the switch doesn't light, and doesn't really bother the remote. That's why you were able to configure the remote even with the switch off. 

This had led you to a misplaced assumption: that you can have dual control between both the switch and the remote.  

No, you can't.  These two things will not play well with each other. 

This is nothing an electrician can fix.  If you hire one, you'll end up paying for a lecture.  This lecture :)  

But there must be a switch that works.

If this is the only light switch in the room, it introduces a problem.  Code requires that there be a light switch in the room in the usual location, and the light switch turns on a light.  

So if this is the only switch, it's simply not an option to bypass it and use the remote exclusively for control of the light.  

If power enters the fan box rather than the light switch, then most likely you can rearrange so the switch controls the light (bypassing the control module altogether), and the fan operates off the remote.  At this point the lighted switch might start glowing like it used to (if the fan's lights are incandescent or LEDs tolerant of obsolete lighted switches).  But if they are not, you can install one incandescent bulb, or you can wire a  Lutron LUT-MLC dummy load/incandescent simulator, in parallel with the lamp (i.e. between switched-hot and neutral). That should bring the lighted switch back. 

If power enters the light switch, and the cable to the fan is /3 type (black white red), then you can also do what I just said, using white as actual neutral, black as always-hot to the remote, and red as switched-hot to the lamp.  If your light switch is a classic /2 "switch loop", and you want /3, that is something an electrician can easily do.