Have you looked at the starter, timing chain, etc?
I have a 2001 Honda rancher esp 350. I had the carb rebuilt and was running great but now it turns over but will not start. I pulled the plug and it doesn't seem to be firing. I changed it and still nothing. Checked all fuses none blown. Any ideas?
Have a look at the following videos. I found them all on Youtube when looking for information about the 2001 Honda rancher esp 350 and I think you might find them useful if looking for info about problems that the 2001 Honda rancher esp 350 has:
The second one just shows a nice new carb install for the Honda rancher esp so it's worth checking that you've got everything set up right.
Use the following image of a carb for these Honda Rancher machines as reference: