If you tune the RX across 10.5 MHz do you hear a relay click? Same thing at 16 MHz? Chances are you do, or did before you lost TX on 20.
Very likely it's a relay or filter gone bad on the TX bandpass filter board. Had that problem with an Icom. RX worked fine but no TX. I have a TS-690 which is the HF plus 6 Meter version of the TS-450 and it definitely uses relays to switch the output filters.
If you're lucky it could be as simple as a bad solder joint. If you can pull the filter board, look for a blackened solder pad under one of the toroids or relays. Clean it up and re-solder... Might do the trick.