If your TV has line level audio outputs (some do not), you can use your old Carver receiver. Assuming that the fidelity of those outputs is okay, it should sound just as good with your Carver as with a new receiver for 2 channel sound. However, the bass management would likely be better with a receiver that has at least Dolby Digital, so a 2.1 system might be better with a surround receiver, though a subwoofer with speaker level inputs can work with what you have, and should be okay.
Of course, you will want to make sure that the Carver still works okay before you count on being able to use it. But it should be able to deal with most speakers quite well, so I would recommend using it if you can.
As for the speakers, I am not sure which ones you mean. Do you mean the AR TSW510 or some other model? Regardless, I have no idea what they are worth and consequently have no idea if it is worthwhile having them refoamed or not. If you particularly like them, then it may be worth it even if their market value is low. Given your situation, I cannot give you the advice I normally give people, to go out and audition as many speakers as they can stand to audition.
But before you plan anything, make sure the TV has line level audio outputs, or you will be doing something other than using that Carver (or computer speakers). Some only have an optical digital output for audio, and for dealing with that, you will want a receiver with at least Dolby Digital.