Your only chance is if you can identify the part number and Google for it. Do you know any independent TV repair businesses?
As far as the TV Portal is concerned, you know it only does BBC iPlayer? It would be a good client to stream from a HDR-FOX though.
The box won't get past its initialisation unless at least one channel can be tuned in - which is OK if you have channels tuned from before the tuner broke. We might be able to get around that with the custom firmware, but I think it is a work in progress (it will get some more attention if somebody has a need). The TV Portal won't work without an aerial signal to set the system clock at boot, so the custom firmware will be needed to get that working too.