Craftsman LT2000 Won't Stay Started Even After New Carb

I bought a used Craftsman LT2000. It worked the day i bought it. The first time I go to use it, it won't start. The guy I bought it from said sometimes the carburetor sticks and is probably time for a new one. Lovely. So I buy one and install it (thank you YouTube!). After everything was reassembled, it started right up, but ran really fast. I lowered the throttle and it stayed almost the same. When I let off the brake, it died. Over the next hour or so, I was able to get it started again several times, but it ran really rough and died within seconds, even while having the brake pressed down. I posted a short 9 second video on YouTube so folks could see and hear the engine as it's trying to run here: . So, any ideas? TIA!