I dont know what they're talking about resin is useless without mat. It is PLENTY strong without any material in it. I got a couple drops on my bumper.... trust me, it's strong. It might not have as much strength or something without matt, but I dont think the matt adds any strength. My view of the matt is simply a medium which absorbs the resin which can then be molded into place. You can't exactly 'mold' a liquid into specific shapes without something to support it. The matt probably does help prevent something made of fiberglass to not simply fall apart when it is cracked - it adds some malleability to the object.
The only reason that there is 'special' matt is because it absorbs a very high amount of resin, thus when it hardens, it is as close to being pure resin as it can be - there are no hollow parts on the inside where the fabric didn't absorb all the way. (this is all my opinion - I could be completely wrong)
That being said - when you buy a gallon of resin, there are two little plastic tubes of 'hardener liquid' that come with it. There is also a small plastic bowl ontop. A small squeedge of the tube into the plastic bowl full of resin, and then mixed together will cause a chemical reaction which will start to harden the mixture. You have about 5 minutes tops in which to do something with the liquid before it hardens or gets too sticky to work with.
In your case - you could build the box, mix a small bowl full of resin, put the box on a side and pour the resin mix onto whatever side is on the ground. It would even out and put a layer of 'fiberglass' on top of the MDF. I would recommend cutting some fiberglass matt to fit each panel, then soak each piece in the resin mixture and lay that on the inside. 'paint' a small layer of the resin over the board before you put the resin soaked matt ontop of it.