The low-impact solution would be to use the stand that comes with the TV and just set the new TV on the shelf where the old one was. This assumes that your new set will come with a stand (my 65" Panny plasma did). The drawback would be that the screen would be recessed a few inches in the cabinet.
If the screen needs to be flush with the opening, then as petew and Woolly suggested, you will need to modify the cabinet to use a wall mount. I have a couple of suggestions: (1) Your cabinet modifications aren't providing a spot to attach a wall mount, they are providing structure to support the weight of the TV. Think about how the new structure will transfer the weight of the TV to the existing cabinet. A couple of screws driven into the sides might not be enough to support the weight of a 65" plasma. (2) How you go about adding structure to the cabinet may depend on what the cabinet is made out of. If the cabinet sides are 3/4" plywood, for example, you can probably trust that screws driven into the plywood from the inside of the cabinet will hold. If the cabinet sides are MDF or particle board, I would be concerned that screws driven into the cabinet sides might eventually fail under the weight of the TV. In that case, you might want to drive the screws from the outside of the cabinet, through the MDF and into the new structure. Or maybe add some PL construction adhesive and screw from the inside of the cabinet. (3) A 65" plasma mounted flush in the opening will significantly change the cabinet's center of gravity. It's going to be front-heavy and may be prone to tipping over. You might need to run a strap from the top of the cabinet to the wall to keep it stable.