Work with your Fire Triangle: check ignition, check fuel, check air. Are you getting a good spark at the plugs? Are you getting fuel? Are your air pathways (intake and exhaust) unobstructed?

If your Fire Triangle is good, here's another thing to look at, if you haven't already done so: check your cylinders and see if there is any coolant in them. If there is, one of two things could be the issue.

1) The head gasket's blown. When my HG blew several years ago, it behaved exactly like that...I had good spark/fuel/air, but when I checked the cylinders, there was coolant in a couple of them. The 4-cylinder Montero/Raider engines are notorious for blowing head gaskets if overheated. Was this engine overheated recently?

2) When you swapped the Weber carb onto the intake manifold, what did you do with respect to the coolant ports that feed through the stock Mikuni carb? The Mikuni carb has coolant running through it. It's my understanding the Weber carb (I've never worked with one on these trucks) does not have coolant running through it. If the coolant ports aren't properly sealed, you could have coolant running into your intake, and this could cause a no-start.