I went over to that m&d link I posted and seen the H35 and it shows both a float or a diaphragm carb for the H35's. (no part number for the float type though but such can be found)
I'm not sure I've ever seen a diaphragm type carb used on a H35 or H50. Most were float carbs
If you can turn the H jet all the way in a get a still get a run is a hint of probably some dried hard crud or the check ball stuck.
Guy gave me a H50 engine not too long ago with no carb/manifold or gas tank. Engine checked good with a leak down and looked engine was clean.
I installed a float clone carb as bsengine suggested to you and used survey flag wire making up the governor and throttle linkages and all came out great. I used a more user friendly softer type wire at first until I got the patterns correct. I happened to have the Tecumseh drop type intake manifold so as to keep the carb low for gravity feed. I seem to remember that maybe the clone carb had idle and h jets as adjustable. The carb was like $12 from flea bay. I used a plastic gas tank from a Briggs engine that bolted on using the head bolts and the bracket. I installed the engine on a rototiller with good results.
If your carb looks like the Tecumseh 631400 diaphragm carb shown in the link I posted at m&d
You can go to a clone float without too much problem since you already have the drop manifold and gas tank maybe.
If getting a clone carb or any float replacement be sure and
measure/match the center to center mounting hole dimensions of the intake manifold mounting holes. (
Replacement carbs are not all the same here)
You can fool around on-line and come up with a Tecumseh float carb part number and then go looking. One with adjustable jets will work on both the 3.5 to 6hp's
Here is a link to how to's for several cabs including some Tecumsehs. Just scroll down and select Tecumseh. Also be aware that some of the Tecumsehs have a intake drop type manifold that the carb bolts to that turns 90 degrees and keeps the carb closer to the engine.
You can see a pic of such at this link also when looking at the Tecumseh carb choices.
http://outdoorpowerinfo.com/repairs/As a last ditch effort on you might consider trying:
If you do not have a HEATED Ultra sonic you might conside doing a 50/50 mix of water and white vinegar and heat to about 140-150F and keeps soaking the carb and using low pressure air. Soak for about 1 hour, neutralize and test if no go back to the
HEATED solution If you have a heated Usonic just keep doing heated runs. The USonic has tendency to break-up hard crud and rust internally in a carb. Use little bit of baking soda in water to neutralize the vinegar water mix when removing the carb for a test. The vinegar will keep acting on aluminum and magnesium and make it turn black and feel gummy/greasy if not neutralized.
Does you carb look similar to this piece of trash over on flea bay? Tecumseh 3.5HP H35 OEM Carburetor NLA (PARTS OR REBUILD) 631400 | eBay
Some float type on flea bay
https://www.ebay.com/b/Tecumseh-H35-Car ... 7023422684