I am a quadriplegic. Would it be possible to power my ventilator humidifier with a battery?
My wife has an HC-150, which is smaller than yours because she only uses it at night.  However, as Olin said, a smaller unit might be an option if you only need it for a few hours.

The other answers talked about the peak current ratings, but what's important for battery capacity is the average current.  My wife's unit peaks at around 90W, but only runs at around a 33% duty cycle at a cold start, and much less than that once warmed up, which means an average power consumption of well under 30W.  She easily runs both her humidifier and CPAP from one marine deep cycle battery for 9+ hours on campouts.  It's heavy, but not so heavy you couldn't mount it to a wheelchair.

The best way to learn your actual average power consumption is to get a kill-a-watt and measure for several hours under typical conditions.  Or just take the experimental approach, buy a battery and the most efficient inverter you can afford, and see how long it lasts while you're safe at home.  You probably also want some sort of level indicator so you don't discharge too far.

Note that peak power is still important when selecting your inverter, because it has to be able to handle that power, plus some margin for efficiency and error, even if just for short bursts.

Something else to consider if you're wanting this for moving around your own home might be some sort of docking/charging station so when you move to a new room you can unplug and replug yourself.  Search for robot charging station for some ideas.

My daughter has cerebral palsy, and I know how important mobility is for her.  I wish you the best of luck in finding a good solution.