Tank will not refill after you flush

I think you have covered it all. Just last flush !

Replace it and see if fixes it. The flapper is designed so that it stays afloat until all the water empties from the tank, then gravity takes over and closes the hole up and thus fills up. If you have a ballcock then the flapper may get trapped underneath when you flush it.

Might be bad gas. Empty tank refill with fresh gas with Stabile. Might have to remove carb bowl clean and reinstall. Flush out tank with a little gas before refilling, disconnect fuel line to flush.

Adjust the float height to allow mor water into the tank before it shuts the valve

Lift the tank lid off, place it somewhere safe for a moment, and look at what happens: If you're talking about jiggling the handle to get the tank to start to fill with water, then it sounds like the chain or rope is out of adjustment. It can't be TOO TIGHT or the water will leak past your flapper (will cause your dripping noise, tank water level will leak down, causing constant refills), and it cant be TOO LOOSE or the toilet won't flush correctly. Since you didn't mention trouble flushing the toilet, I think that it may be a little too TIGHT. When you jiggle the flush lever-it is supposed to pull a chain or cable to open the flapper at the bottom of the tank. Flush the tank and watch what happens-all the way through to refilling the tank with water and shutting off the water refill valve-Does the flapper get stuck on the chain or something? It is supposed to fall back down to allow the tank to refill after flushing out your toilet. Does the chain look very loose? The dripping sound you described indicates that the flapper is not sealing 100%. The flapper is very easy to replace, you just have to get the adjustment set for when you flush the toilet how sensitive you need it. You amy have to play with it a little bit before you get the adjustment correct.

Hope this helps!

Yes, it will run up your bill! Sounds like the float is hanging up. Take tank lid off and flush, watch the float and if your tank fills quickly but does not stop, bend the float arm to angle the float down further, this should allow your water to stop coming in much quicker. The other possibility could be if the plug at the bottom does not seal correctly after flushing, if so, the water will leak until the plug sits down all the way.

I had the same problem. The fix cost me 50 cents (literally). I just placed a quarter on top of the Blue and White flush buttons (not sure of the technical terms) inside the tank and now it flushes properly. It seems that the 2 plastic poles the extend from the faux chrome buttons are just a bit too short.
Hope this helps