Snowblower electric start doesn't work

I have a snowblower where you can plug it into the mains to start it. When you push the button all I hear is a grinding noise. Using the backup pull chain I can start it right away.

What might be broken and how mechanically inclined do I need to be to fix it?

When you push the start button a gear on the starter pops out and engages the flywheel on the engine. Either the flywheel or the starter gear is worn. Possibly both, but probably the gear on the starter is plastic and has failed. It should be easy enough to remove the starter and investigate.

remove the starter. inspect its teeth and those on the engine flywheel. if both look good then clean and lube the starter gear so that it moves in and out fully and freely.