| Your idea for epoxy isn't the best for what you want. The problems are these:
1. Epoxy is a 2 part adhesive that has a limited working time before the catalyst and hardener begin to get too thick for application. You would have to mix enough to do an entire cabinet and then work quickly enough to finish be fore the mixture hardened. Too much room here for a mistake or poor application.
2. After complete curing, epoxy is somewhat brittle and wouldn't do well as a coating that could, forseeably, take an impact. I would suspect that the layer would crack and eventually give up pieces.
That said, there are a couple of excellent solutions to your problem:
1. Bedliner - Sold through automotive stores, this product is a roll-on, one-part polyurethane coating that will encase and waterproof your cabinet. You might find it under the name "Rhino Coating" This stuff is EXTREMELY tough (hey it's used in pick-up beds!) and comes in several colors. When rolled on, it creates a nice textured surface, not unlike the Tolex fabric it would replace. It isn't the cheapest stuff in the world but it would be less expensive than epoxy to do the same area.
2. Indoor/Outdoor carpeting - Found in home improvement centers, this is a step up from the usual carpet covers that most cabinets have. The type you want comes with a fairly hard "backing" that acts as the perfect glue surface. I've use this with great success on my last cabinet and will likely do it again. The best material will have some small "ribs" in the weave that can be oriented to the cabinet and look very good. It doesn't have the "fuzzy" appearance of other types of carpet. This material is applied with spray on contact cement and, once attached, is also very, very tough. After you've finished gluing the stuff down, you can re-install your hardware and go to town! | 
