Try gradually warming the glue line with a heat gun (the real thing, not a hair dryer) while pushing carefully from below. Go slowly with the heat gun to avoid paint damage.

I can think of a couple of ways to push on the top. One is to drill those triangular braces at the corners and put a 3/8" bolt through each of them with a fender washer and nut on top of the brace (between brace and countertop). I'd probably also put a steel electrical junction box cover or something similar between the bolt and the top so the bolt doesn't just dig in.

As you warm the glue, gradually tighten the bolts to push the countertop up. Careful not to push too hard and break the braces.

If the cabinet bottom is solid, you could also push with 1 or 2 automotive type hydraulic or scissors jacks, using lengths of 2x4 between the jacks and the top. You might have to glue the 2x4s to the top with hot glue so they don't slip.

Once you have the countertop loose in back, put something between it and the cabinet (a few large bolts or something) so it doesn't stick itself down again while you move your tools and repeat the procedure on the front glue line.

@DavidR thank you for explaining that. The heat gun to loosen the glue seems easy enough, but the rest sounds very difficult, and I've never used a jack. Is there someo I could hire to do this?

The glue is securing particle board to particle board- it will give pretty easily. After disconnecting and removing the sink I would start at the back where you already have gaps at the glue blocks- slip a pry bar in there and pop it up

@Joseph Corlett, LLC really? That sounds too good to be true, but I'll give it a try. Maybe I'll get lucky!

@HALLETT & Co, I'm afraid the cabinet particle board will give first since its the thinner of the two. I will start slow and see how it goes. If I get it off successfully, I will need to hook up the sink again to use until my new countertop is ready. Any precautions I should take for that?

Will the new counter be delivered and installed?..if so perhaps the installers can remove the old top?..

Perhaps, but I'd be afraid they would man-handle it. Mainly, I need to repair the wall behind the counter top. When I took off the old backsplash there was a big hole in the wall behind it. Since I'm not doing a backsplash with the new countertop, the wall has to be finished before they install it.

I would cut thru the middle of those particle board riser blocks with an oscillating tool. The short pieces of particle board that are between the top of the cabinet that the counter is resting on. Will need to remove the sink first so you have room to get the tool in there. 5-10 minute job.

For a one-off job, buy a cheap one if you don't already own one.

https://www.harborfreight.com/Variable-Speed-Oscillating-Multi-Tool-63113.html?ccdenc=eyJjb2RlIjoiMjY3MTM4MTgiLCJza3UiOiI2MzExMyIsImlzIjoiMjcuOTkiLCJwcm9kdWN0X2lk%0D%0AIjoiMTE4NTAifQ%3D%3D%0D%0A&cid=paid_google|PLA+-+All+Products|All+Products|63113&utm_source=google&utm_medium=cpc&utm_campaign=PLA+-+All+Products&utm_content=All+Products&gclid=EAIaIQobChMI86aMuZK-6AIVip-fCh2eNQlEEAQYAiABEgLz0vD_BwE

@ci_lantro I've always wanted one of those. That price is nothing compared to having to buy a new cabinet. Ok, I will try that. Then probably kick myself for not buying one a decade ago.

You won't regret owning one. They're almost an indispensable tool.

I bought a Harbor Freight cheapie several years ago. Doesn't see a lot of use but has held up fine. But it is LOUD. Hearing protection is a must. One other thing that surprised me--they're easy to control. Don't absolutely have to but first time out, good idea to practice on something that doesn't matter before taking on the vanity project.

Are you sure that top piece is not just either screwed on or siliconed I bet that counter was prefab and is a separate piece.

@Patricia Colwell Consulting, I wish! I removed the sink and can see the dark-colored construction adhesive between the countertop and the cabinet.

@ci_lantro, wouldn't you know, the valves started leaking when I disconnected the sink from the supply lines. Had to change the valves, but one is still leaking, so now I have a plumbing project on top of everything. Ugh.

@Joseph Corlett, LLC, stiff scraper technique is not working. I can't get a good swing with the hammer underneath there. The adhesive is like tire rubber. Won't even dent. Will try a heat gun next to see if it will soften.

Put a multi-tool on the glue joint please.

The glue they use to adhere the top to the cabinet is stronger joint than what is there in the top construction.

Simply buy a demo crow bar and hammer it in between the blocks and counter NOT the block and the cabinet. It will easily break free. Particle board is weak and will splinter into pieces.

If you have a saw you can cut out the center of the counter giving better access to the blocks. Also you would be separating smaller sections.

Fix your valve you can flood your entire home.

@Joseph Corlett, LLC, @GannonCo, just bought a multi-tool to remove the countertop. Will practice on some scrap first. Put a new valve on the supply line and the leak is fixed.

My projects never go like the YouTube videos where everything is done in 10 minutes.

Yeh, that always happens with the valves. You're supposed to operate the valves once a month but NObody ever does that.

Countertop is off! Now just cleaning up the stuck on bits.

Goodie!

You can buy caps for the shut off valves if you don't have time for a replacement right now. Modern ones are typically 3/8" compression (which is a different thread that iron pipe).