After the merge, will miners have an incentive and/or the ability to continue mining the old PoW coin?

The point of the whole transition is that miners stop mining and wasting electrical power and hardware.

Thus: no.

Sell your hardware, build a validator and start staking.

When the consensus alghorithm changes to PoS, the old miners will no longer play any part in Ethereum mainnet (the canonical blockchain). Miners could try to fork Ethereum, but then someone with at least some technical knowledge has to modify the code and remove the difficulty bomb. Or they could switch to other chains with similar mining algorithms, but that is likely not going to be profitable.

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