Clogged venturi tubes or other fuel circuits could be an issue here. When you have the time, look through my article on rebuilding the BBD. Also, regarding the O-ring, did you remove the bowl vent, too? Look at that illustration near the top of the article.
Before you get involved with the carburetor again, disconnect the fuel hose at the carburetor side of the fuel filter near the carburetor. Safely route a piece of fuel hose to a can away from spark and heat. (You may need to cap the fuel filter return hose nipple to prevent a leak.) Remove the high tension (spark plug gauge size) wire from the distributor cap to the coil as a safeguard.
Have someone crank over the engine. The fuel pump should be moving fuel. The normal volume for your pump is 16 oz. in thirty seconds with the engine idling. Since you cannot get the engine to run, the cranking volume will be less but should be a steady flow, spewing in pump strokes. If you have a gasoline pressure gauge, the fuel pump pressure is 4-5 PSI on your pump's application. You should have the 3-pipe fuel filter and all EVAP components hooked up.
If there is no fuel moving through the pump, the fuel tank pickup could be plugged, or there might be a restriction in the system (doubtful, the engine ran when you shut it off last year). Then there's the often overlooked issue with the emission system and possible trouble with the EVAP hoses and components that can cause a fuel lockup in the system. We'll talk about that if you're not getting fuel to the filter.
I'm not quick to condemn parts and start the "parts replacing" strategy. One item that can cause havoc on the 4.2L engines with EVAP, however, is the fuel tank cap. If the cap is not pressurized and sealing properly, there can be a fuel supply problem. I'm bringing this up, because in the worse case scenario, there can be little or no fuel to the carburetor bowl.
For the moment, let's not "borrow trouble", there's plenty available if you cannot find a problem at the carburetor's fuel circuits. Since you do have a carburetor kit, I would definitely follow through with the rebuild, using my article and this forum if necessary to assist. There is a lot of creative misinformation on the web about the BBD and how you should strip off the Sole-Vac and other components. This is a senseless approach unless done systematically, and that's not easy with so many components and functions overlapping. Rebuilt to factory, "blueprint" standards like I describe, including the Sole-Vac system restoration with alcohol as a cleaning agent, you can get great results. You do need to make sure all of these components function properly, though, and that the fuel, vacuum and spark systems interact as designed. Not always easy with a 1980-90 4.2L Jeep inline six!
If your Jeep CJ-8 Scrambler is stock and intact under the hood, consider yourself fortunate. Any missing or defective pieces within the fuel/carburetor, vacuum, spark control, fuel metering, EVAP or exhaust systems, plus the electronic modules and wiring, will present a troubleshooting challenge. While many CJs and early YJ Wranglers have been converted to Mopar, Howell and MSD Atomic EFI systems (click here for details on all three systems in my 5-page article on the MSD Atomic installation), you may not want to go that expense. I'm not a big fan of the Weber carburetor "cure", however, that's a less costly alternative.
To instill owner confidence around later CJ and YJ Wrangler 4.2L engines with the BBD carburetor and OEM spark system, I like to use this metaphor: We tested these vehicles over the Rubicon Trail in fully stock, showroom fresh form. They behaved like any other carbureted engine in terms of side slope flooding and altitude sensitivity; however, they ran very well. I'm a restorer and believe that the OEM system, when working properly with its integrated components intact, can be a success story.