I replaced my battery in my 13.5 hp Murry riding mower. I got two starts on it and the battery died. I had the battery tested and it was good. I was told the starting solenoid would not be the problem. The battery is not getting recharged. The key is in the off position, my lights are not draining the battery. I was looking to see if the alternator is bad, but I don't think this engine has one according to the manual? Any other suggestions?

Get a v12-Volt test meter and check your battery for 12+ volts not running. Then start the engine (you can jump with auto) and check voltage to see if it is higher 13-14-Volts.

The battery's available tend to be poor quality and is not unusual to have a new one fail. (new being 8 months or less)

Right on, thanks for the tip. I did get a tester and I had the battery tested for a second time at a different place and the battery was good. I installed the battery and when I connected the posts, I looked at the terminal leads and the POS had some acid corrosion on it. I cleaned it up and connected the battery then put meter to it. It showed 12+ V. I started the mower (without boost from auto), then checked meter; it read 13+ V. Everything is working great. Thanks for the help.