I don't think that would be possible.
These are the smallest digital TV receiver modules I can find:
**broken link removed**
Detailed info about Mini ISDB-T Digital TV Tuner Module with MPEG4. Contact Taiwan TV Receiver & Set-top Box supplier-RICHVIEW INTERNATIONAL CO., LTD. for on Taiwantrade.
www.taiwantrade.com
There are different versions for the various digital TV standards used in different parts of the world.
(They are incredibly complex devices and it not practical to try and build the actual receiver/decoder from nothing).
In addition to something like that, you need a computer (a microcontroller) to configure and control it, emulating a TV remote control and somehow adding the physical controls to do that to the TV casing.
Is there physically room for all than in one of those Sony receivers?
A more practical option is just get a handheld digital TV such as this:
Amazon.com: 3.5" Digital Prism ATSC-300 Portable Handheld LCD Digital TV - ATSC Tuner w/FM Radio & Car Adapter (Black) : Electronics
www.amazon.com
You could possibly rebuild one of those in to the case from a Sony, to keep the retro appearance?
Is the digital TV signal where you are even strong enough to receive using a small built-in antenna? Where I am, it needs a large rooftop antenna to get a good signal and range of channels. An indoor antenna does nothing.