Bought a non running 96 polaris 300c atv guy rebuilt engine and installed rings wrong broke piston on start up,repaired broken parts ,had running,sluggish,hard starting,rode it a couple times after start up ,died will not restart acts like out of time,2cycle motor,

severe knock / rattle under load
excessive smoke as the crack normally occurs at the oil ring groove dropping that ring into the sump
describe the symptoms that you have as if it is a rattle under acceleration that will be detonation and is a air/fuel mixture problem or ignition timing too far advanced the skirt is what maintains the alignment of the piston crown so if it is cracked /broken off you will have no doubt of the noise at idle and at rpms
pistons seldom fail because of the engineering and material used so it would have to be an extreme operation that would cause the failure
other similar noises can be from loose valve seat insert
piston hitting valve head from failed valve spring big end bearing cam lobe worn out

This should be for 2 cycle oil injection , find a owners manual online for proper oil ...

double check the timing and timing chain tensioner. maybe a leak on the intake manifold?

Carb, is still plugged or your float is stuck or not adjusted properly.
Check the attached links,Manuals and guides, Good luck with your Bike
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Service Manuals for Download in PDF
ATV Service and Repair Manuals
http://www.carlsalter.com/motorcycle-manuals.asp

did you remove the carb and clean in a vat and rebuild it or just sprayed a can of carb cleaner thru it. needs toom part and cleand and rebuilt... this is a comman issue with those models

If you need further help, reach me via phone at https://www.6ya.com/expert/allen_b068623c5003aa4b

Hey Brandon, there could be several things... one is you put the piston in backwards... the arrow goes toward the exhaust..(if there are holes in the piston, they go in the back).., you installed the wrong piston..or..skirt was too long.., you left something inside the engine..(dropped one of the circlips in the engine).. the rings were installed upside down..,one of the circlips came out..., you got a bad piston..(never seen this happen).., the cylinder needed boring and it had so much clearance that the skirt caught on the intake port lip...

OK...Brandon, repairing this engine correctly is going to require a COMPLETE DISASSEMBLY - there are tiny tiny bits of aluminum in the main bearings, packed in between the main bearings and crank seals.. its in the main rod bearing..and its all in the bottom of the cases... THE ONLY way to effectively remove ALL this is to pull it apart.. this is not a hard job, but if you have never done it, PLEASE take it to a qualified professional.....it requires several special tools... .they may/should be able to tell you what happened to cause it too..
IF you do not do all this, you WILL have premature ENGINE FAILURE AGAIN!!!! and this time it could be worse!

Could be a rod. Not going to be that easy to do. Valve noise is not a knock.

First - Did you find ALL the pieces of the broken piston...if not...STOP and FIND them.. they are in the bottom of the crankcase...you engine WILL NOT live long if you have not gotten ALL the pieces--even the TINIEST ones out!! You mat have more damage than just a broken piston.. something caused it to break.. you may have cracked the crankcases...may have damaged the main bearing(YES) and/or damaged the crank bearing.. see if gas in leaking into the transmission oil.
There is an arrow on the piston that faces toward the EXHAUST port. If there are hole(s) in the piston, they go towards the INTAKE.
Do some more searching and repost the results for review!

I don't have a trial boss 250 but on most 2stroke engines you should never see the top of the piston through the intake port when the carb is removed as the piston doesn't go low enough, thats by design, its the exhaust side you need to look through to see the piston top(crown), if you remove the exhaust to have a look check the condition of the piston rings while there