Got a new house and bought a used LT1000. It ran fine for 2 months and then it started running rough and backfiring. It now backfires and will not start. Here is what I’ve done so far:
- replaced the carburetor
-replaced the plug and validated there’s spark
- adjusted the valve clearance
- replaced the fuel filter
- confirmed the flywheel key is intact
- replaced the fuel filter

What else can it be?

What BRAND ENGINE, what HP, what MODEL # of the engine???
 
Previous history???? (Just got it, sat in the rain, etc)
 
 
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It’s a Briggs Stratton 18hp OHV Intek engine. 31H777-0605 E2 050701ZD

I don’t know the previous history but it ran fine for a few months then sporadic backfiring with pulsating idle. Last week it got worse and it now no longer starts and backfires when I do try.

https://www.jackssmallengines.com/jacks-parts-lookup/manufacturer/briggs-stratton/briggs-stratton-engine/200000-399999-series/31h700-to-31h799/31h777-0605-e2 
 
Does it backfire thru the exhaust or intake?
 
Have you checked the valves, that their opening and closing and what spec 
( in thousands) are they set at ) ?
 
Will it fire off with a spritz of carb cleaner down the intake when cranked over?
 
 
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I did set the valves to the appropriate specs. I think it was .004 and .006.

It backfires thru the intake. I tried starting fluid and it backfired.

Seems the intake is not fully closing or is out of time.
 
Can you do a "leak down test"?   
A compression test too, but the leak down would be more conclusive..
 
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I don’t have the equipment to do a leak down test. I’ll do a compression test. I spent $500 on the mower. Not sure how much more money I want to throw at it.

I was hoping it was something easy and restively inexpensive to fix.