Won't start without prime, runs rough. Stalls on acceleration

That sounds like a failed accelerator pump in a carburetor. Those come in rebuild kits which are rather inexpensive.

Rats. Then start with checking for diagnostic fault codes. If there are none, you'll need a scanner to view live data. In particular, look at the throttle position sensor for proper response. If you have a mass air flow sensor, be sure there's no loose hose clamps or other leaks in the tube between the throttle body and sensor.