What may cause a strong smell of paint thinner like odor and no power to master in a Piper Warrior?
You've got two unrelated problems: The battery and the smell.

The Battery

Battery electrolyte doesn't really have a "smell" to it - at least not one you're going to notice in the cabin easily. If you open the cell caps on a newly-topped-off flooded battery and sniff you'll get a feeling for what the electrolyte smells like.
If you have a sealed battery you're not going to smell electrolyte unless the battery completely loses its mind and vents a large quantity of electrolyte - you'd definitely notice the mess in the battery box if that happened.  You may notice it in a conventional flooded-cell battery if the battery is overcharged (from high bus voltage, or from trying to charge a flat battery after jump-starting the plane), but again it's not going to be readily apparent in the cabin unless you've lost a large quantity of electrolyte or you're really boiling the battery from an over-charge.

If your battery's cells are full (or it's a sealed battery) and you didn't leave the master switch on then the likely cause of it being flat is that it's old and can't handle the low temperatures of winter anymore (or if it's a new battery it may have developed an internal fault and discharged itself). 

If you left the master switch on putting the battery on a charger/conditioner overnight can usually bring it back to good operating condition. You can try that on a flat battery from an unknown cause too: The good charger/conditioners will warn you if they think the battery has an internal fault. If an overnight charge doesn't resolve the issue then you're going to need to replace the battery before further flight (and frankly replacing the battery is cheap insurance against getting stranded somewhere, so it merits consideration anyway).



The Smell

The smell of 100LL changes as it evaporates - lighter aromatic components vaporize faster, and will waft out of the cabin more quickly, leaving the smell from the heavier hydrocarbons lingering.
As you discovered avgas that's been evaporating for a while loses the characteristic benzene/toluene scent we're familiar with from sumping the tanks and has the general odor of turpentine/conventional mineral spirits ("paint thinner").

The first thing to check in the PA28 when you smell something like this in the cabin is the fuel selector valve, as it's a common failure point particularly in cold weather: The packing/tapered plug in the fuel selector valve has shrunk in the cold, and you're leaking fuel around the shaft (which is then soaking into the carpet and evaporating off, giving you the smell in the cabin). Other aircraft may have similar failure modes in their fuel selectors, but I'm a Piper guy so I can really only speak to their systems and associated quirks :-)

Since your shop identified the fuel selector as the problem it's an easy fix: Rebuild or replace the fuel valve and the leak will stop, probably for many years.  (Piper Service Bulletin 355 is relevant to this issue for older Pipers - the O-ring identified in the exploded diagram dries out and shrinks/cracks, allowing avgas to leak around the shaft. There may be something similar in Piper's service documents for the Warrior II, I'm not sure if it uses the same internal valve or not)

Another common failure point would be the O-rings around the primer plunger in aircraft with a mechanical primer (anything before the Warrior III).
This doesn't normally manifest as a lingering smell in the cabin but rather a smell when you operate the primer plunger (usually also accompanied by the plunger being stiff/hard to operate). Much like the fuel selector it tends to manifest when the weather gets cold and things shrink or become brittle, and the cure is to disassemble and appropriately service the plunger mechanism (replace the O-rings and re-lube the mechanism with a fuel-safe lubricant).