Not to zero. I'd personally pay $1, probably more, for even 10% of all Bitcoins, just for the novelty. If there were no miners, maybe not much more than that, and I'd want the current private keys.

I'm guessing there's at least someone that'd pay a few million for all of Bitcoin, so maybe a $0.10-1.0 floor, easily? Would be illiquid and hard for small holders to sell though.

Also, quantum computers do not break Bitcoin entirely as in previously unused addresses are safe. You'd need a way to quickly generate keys matching a certain hash. Otherwise you need a ton of hashing power, too, to rewrite the part of the chain created in the time a spend-of-interest was created and you generated matching keys with your attacking machine. Seems like something that can be upgraded assuming a QC-resistant crypto scheme exists.