For starters, go to the kohler web page, sign on as a guest then download the parts, owners & repair manual for your engine.
Go to Troy built and downlaod the parts book for your mower as it has the wiring diagram in it and we like to use part number to describe parts to avoid confusion.
Arm yourself with a can of carb spray ( you will use it as starting fluid ) and a red spark tester as you have a twin, 2 would be better.
The ones I use are Oregon part No 42-087
Hook the testers up then start then engine, choke off by spraying SHORT SHOTS of carb cleaner through the carb.
If it starts and you can keep it running ( badly ) for about a minute with repeated SHORT SHOTS then you have a fuel problem.
While you are doing this keep your third eye on the spark testers, both should be flashing at around the same rate but not the same time .
If the replacement carb was the same price as a rebuild kit then it is a Chinese knock off and there is no reason to believe it will be correct for your engine or even work .
So put the old one back on.
Clean it as per the instructions found here
http://outdoorpowerinfo.com/repairs/
When you dig up the engine number ( it will be CV something ) and the mower number from the tag under the seat both of which you will need to get the correct manuals, post them here so we know which engine we are trying to walk you through fixing.