Could someone restart zk.money if they wanted?

My understanding is that zk.money no longer has a sequencer running and the keys to the contracts have been thrown away. Is there anything that would prevent an independent party from running a public sequencer and restarting the chain?

I’m not talking about just enabling withdraws, but fully restarting the chain and running it as it was before it was shutdown.

Yes, someone could continue to build blocks and process transactions for Aztec Connect. The code for the project is available here: GitHub - AztecProtocol/aztec-connect: aztec connect repository

My understanding was that zk.money v1 could be restarted, but Aztec Connect could not be because sequencer blocks are no longer supported and only withdraws are allowed? Is this incorrect? Can someone actually publish new blocks for Aztec Connect?

That is incorrect, you can publish new blocks to Aztec Connect.

Publishing new blocks may be possible, but the rollup processor contract (Aztec: Connect (0xFF1F2B4ADb9dF6FC8eAFecDcbF96A2B351680455) | Address 0xFF1F2B4ADb9dF6FC8eAFecDcbF96A2B351680455 | Etherscan) appears to have deposit limit of 0 set on every asset type, and the rollup is currently in “capped” mode, which means those asset caps are respected.

Correct, you cannot deposit into the rollup. But if you already have funds in there, you can create transactions and blocks to move funds around.