[Bluexrx]

I ordered my Trailmaster 300 XRX last-month from Moto-Buys, my first ever Go-Kart. Anyhow, ordered it on the 5th and received it on the 12th. Set it up several days later and fired it up. Had a difficult time getting it started, but was able to run for 6-10 minutes on 3 occasions before it overheated and shut down.
Then, after several days of not being able to start it, it fired up again. I ran it around my house for two miles. After that it wouldn't start again for two-weeks. I removed and cleaned-out the carburetor, reassembled & remounted it today and sure-enough it fired up!
I ran it for a mile or so before realizing that the red-light (overheat) light was on again and shut it down. After two hours I attempted to start it again, and nothing. Turn's-out the battery is dead. I had always noticed that whenever I attempted to start it during those previous two-weeks, the "Battery Tender's" red light was on, just from the starter engaging. Should I replace this battery, or might it be a component failing to re-charge it while it runs?
Any suggestions/recommendations from experienced Buggyist's, would be very much appreciated...

Thanks in advance..!