Small Engines (Lawn Mowers, etc.): Mower wont turn over, stator winding, turning the key

Question
I thought I had enough gas in my mower, but I didn't. After running it out of gas and running to get more, I filled it up and tried to start it. It didn't start right away and acted like the battery was going to run down. I let it set for about a half an hour and tried again. It turned over freely but didn't start. I held the key over for about 30 seconds. now I have a fully charged battery, but when I turn the key over all it will do is click. The wire running from the battery to the solenoid gets really hot after turning the key over. Is the solenoid the problem or did I burn up the starter?  

Answer
Hi Kevin
Unfortunately - yes the starter is toasted.  If you know a shop that rebuilds alternators, they miiiight be able to rebuild it- if all it did was melt the brushes.  If the stator winding is smoked- look for a new starter on ebay
sorry man- Lemme know how it turns out.