Check out WeldingWeb, it's an online welding forum. There is a section on there dedicated to Hypertherm. Congrats on the purchase! I just picked up a Powermax 380, and have cut a bit of material already.
Clean and dry (seriously) air will be your best friend when using a plasma cutter. I've got a water separator and a regulator right at the compressor, and attached directly to my plasma cutter, is a dessicant dryer. You'd be surprise how much condensation a hose can pick up while laying on a cool concrete floor. Moisture or other contaminants in the air source will eat the consumables in the torch pretty quickly.
I'm not sure if you have pulled the torch apart yet, but it may be a good thing to take off the cap and see how everything looks. Check for obstructions in the swirl ring, that there isn't alot of wear on the electrode, and that the hole on the nozzle is still round. Just for the heck of it, I'd suggest throwing a new nozzle and electrode in for good measure.
I wouldn't run anything off a generator without at least a 7000W rating. The motor load when a compressor fires up is quite a bit. If the generator can't produce the required voltage, then the amperage draw increases significantly. I would however recommend running the plasma on 220 if you have the ability to do so. Be sure that the voltage switch on the back of the machine is set to whatever you're going to use.
If your work-lead is not in great condition, then I would suggest getting a new one, or repairing the one that came with the machine. As in welding, the ground is a big part of the puzzle.
Is there any of the indicator lights on or flashing while using the machine when you start having problems?