Go through Craigslist furniture postings and you'll find an amazing array of entertainment cabinets for sale. The reason they're all up for sale is that people are buying new TVs, none of which fit into that squarish space that their old CRT based tube television sat.
I had a crazy idea on what to do with those old units that are going very cheap. If you have a large living space, preferably a warehouse loft style one, then buy a bunch of units and cover one of your walls with them. You'll lose some square footage in the room but have tons of shelf space and an excellent conversation piece. Just an idea.
Now for a more pertinent idea, that is, solving the dilemma of making that new flat panel TV fit in the existing entertainment cabinet you don't want to give away for spare change. There two solutions.
The first is to create a matching false wood panel that would be installed in the front of the cavity. Then you could install a wall mount onto that panel and hang the TV. Sure, the width of the TV will be more than the existing space. You'll have to make that judgement call as to whether it'll pass the good interior design test. I've seen it work well and not so well.
Depending on the value of the existing cabinet you may want to hire a cabinet maker to modify it so that the wood matches. And if you do it yourself, make sure you secure that false panel well so that the weight of the TV doesn't pull the panel from its place. Oh, and have some fun with it. Throw a newspaper and some current things in the space and treat it as a kind of time capsule, sealing it up until some distant date in the future when you eventually do get rid of the piece.
The other possibility is to buy the more expensive full motion mount with scissoring arms that let it extend from the wall or in this case the back of the TV cavity. You won't be able to retract the arms unless you buy a small flat panel and that's unlikely. Instead, like the first option, the TV will span further width wise than the existing hole but will now appear to be floating in space.
It's mandatory to have some very strong backing wood behind the cabinet where the mount will attach to since the torque from the weight of the TV being extended will cause heavy strain on that rear wood panel. And make sure the extention arms are long enough to extend beyond the depth of the cavity.

If you have a question or if I may be of service call me at 440.724.0558 or email me at radiohannibal@gmail.com
John Hannibal