How do I take apart an older model bathroom faucet?

Question

I'm trying to take apart a leaky bathroom faucet. I've isolated the leak to the cold valve, but I cannot figure out how to disassemble the faucet. I've watched several helpful videos and read through some helpful questions, but I've got an older faucet and they don't apply. Here's a pic:

So far the things I have tried are:

• I've taken the screw out of the top, but that does not seem to loosen anything
• I've screwed the short metal rod from the handle back in the side, and used that as leverage to yank and twist, but that doesn't help me pull the top off
• I've rotated the tap fully clockwise (the direction that turns the water on) several full turns around, and it does not appear to be loosening
• I've screwed the short metal rod from the handle into the tap and used a crowbar to hit the tap upwards, but it does not move up

I don't see any other places/parts/screws I could use to disassemble this. How do I take this apart? Thanks.

Edit: I added two more steps I've tried to remove the tap

Answer 1

Remove the screw from the top completely, and then pull straight up on the cold water tap. It may take some pressure but it will come free. Under that you should find another cap, screwed on, which will be holding the cold water stem (aka valve stem) in place.

Answer 2

I appreciate the answers folks, but after wrestling with it for a while (and denting it up while I was attempting to pull the tap off), I just went ahead and replaced the whole faucet.

Answer 3

Older faucets in theory should just come off using a screwdriver. Unfortunately, with time they corrode and parts rust together, making it difficult or even impossible to remove without damaging the faucet.

You just want to remove the screw, then use a flat edge to wiggle the handle loose. Put a cloth underneath to avoid scratching. Wiggle for a bit and try to pop it off by pulling upwards.

Sometimes, there is no way to do this without breaking the faucet, so be prepared to buy a new one.