To identify which version it is, does the bar mount have 2 studs with 18 or 19mm bolts and does it say TS 08, or TS350 super? The early TS350's came with a 47mm or 49mm piston. I believe the 47mm will only fit a T27 round key and not my hex socket. The ignitions are a dime a dozen, the saws aren't worth more than $50 non running and found at the scrap yards ALL THE TIME. The early TS08 may have points AND GOVERNORS. Yours will be electronic. Bearings are 203's same as GM alternators, PS pumps, Clutch pilots and most ceiling fans. While you have the carb off, pull the hose and check for collapse. Last week I had one with a bad flywheel key that tor up a flywheel. Wobble your clutch up and down to check the bearings. It is a wise investment to buy a set of OEM seals, and do the bearings to make it reliable. I find more often than not these are scrapped due to fuel issues and silly things.
If you need a part PM me, I have about 75 of these.
Other than being a few pulls more than a 400 the 350's ARE MUCH BETTER ON FUEL IMO if you are cutting brick and don't need 14" Literally bullet proof and easy to fix. Also throw a few drops of oil on the clutch needle bearing.
The TS510 was a great saw, I would prefer the TS700 over the TS800's as they tend to crack crankcases bad = no saw. To the upper left you will see our technical director doing some 400's at age 8 or 9.