The cheapest way to carry a lot of power around without cords is probably going to be lead acid batteries. Let's figure out your power usage, and then go from there.
The basic system is going to look like this:
Battery -> DC-AC Inverter -> Projector
We need to identify the load on the battery before we can estimate run time, so let's start with our loads. I was able to find a page that lists the operating power consumption of the projector as 224W. I'll estimate that you don't have a power-hungry laptop, and estimate power consumption at 40W. (You didn't include any current figures for the power supply, so I'm guessing.) This gives a load of 265W for the inverter.
I found an inverter that meets your continuous load requirements, and I calculate that it has a full-load efficiency of 78%. With a load of 265W, that results in an input power of 340W. This is effectively an average current of 29A at 12V.
The final step is to select the right battery. Battery capacity is measured in Amp-hours, and for every 30 Amp-hours you will get about 1 hour use. This sealed lead acid battery is 75 Ah, and it will last you for about 2.5 hours.
If you want to increase your run-time, you can:
- Find a more efficient / lower power projector
- Use a lower-power laptop
- Consider using a 12V laptop power supply
- Run your laptop off it's internal battery (thanks @jpc)
- Find a more efficient inverter (The one I linked to was the first I found)
- Buy a larger (Ah) battery
- Put multiple 12V batteries in parallel
All this should fit reasonably well on a hand cart of some kind. The battery will be heavy - the one I listed was 60 pounds. If this sounds like too much work/danger/weight, invest in a really long extension cord.