Starter won't start
 

I went to start my Miata last week. It was kind of cold out (-37C). The engine turned over about twice really slowly and then nothing. Tried to boost it, still nothing. Took out the battery to charge it and wait for a warmer day.

Today installed the newly charged battery and tried again. It was not too cold today (-20C) but still nothing. Hooked up a chain and pulled it behind a pickup truck. It started no problem. Everything works properly, except the starter.

Looking for suggestions on where to look for this problem. Is there a fuse on the starter circuit?? What else could it be?? The battery is fine. All the accessories work fine.

sounds like starter to me.

Or just the starter solenoid if you don't even hear a click when you turn the key. There's a red wire with a spade connector going to it on mine, you could check that first.