You can't "mine" using Proof-Of-Stake (POS). I don't know which algorithm they will choose when/if they eventually do switch to POS, but one method is that the wallets that store the most ETH have a higher chance of being selected to perform some inexpensive computation. You get paid for performing these computations.

So to answer your question, you could potentially use your old PC to host your POS wallet and earn ETH. The amount you will earn will depend on how much you currently have and how long your are connected to the network.