I did a “refurbishment” to my used Epiphone Les Paul (fretboard cleaning/oiling, new pickup surrounds, new strings, new knobs, new bridge, new pickguard, wax & polish). Now that everything is put back together my neck pickup doesn’t work. Well, it works, but barely. With my amp turned way up I can hear it a little bit. Any idea what this means? Did I shake something loose? Is it fried? Could it actually be the toggle switch?
Pickups are fairly robust, so it's most likely to be an issue elsewhere. Check for loose wires, bad contacts at the switch and bad pots.
After looking around the interwebs I'm inclined to think the toggle switch needs to be cleaned, or better yet, replaced. It seems to be the most common issue with Epiphones as the switches are crap. I'm not surprised because I have experienced some problems with the toggle.
You can swap the wires on the toggle and if your neck pickup works and your bridge does not, then its in the switch.
It looks similar to the switch in the photo. Great suggestion Fastmerc. I will try that.
The contact points of these (and most other) switches are made of a silver alloy whose oxidation is almost as conductive as the clean metal. The reason that skeleton and box switches are crap is because they rely totally on the spring action of the leaves to operate properly. Over time the spring action wears out and the leaves only make intermittent contact. To fix this, you can bend the failing leaf back into contact.

You can clean the points by simply wiping lightly with a damp or dry cloth. NEVER use a wire brush or a file.

I think that the problem more probably a bad connection at the switch or somewhere else. Trying re-flowing all your solder joints if the switch tests good.
I took it to a local tech. Turns out the toggle switch is fine. The pickup was grounding to the conductive paint inside the pickup area (my words, not his, as per my uneducated understanding). Anyway, he fixed it and looked everything else over for any other issues, and charged me $15. Now it works great and sounds great. But now my brand new Peavey amp is dead, which is another story in another thread.