I'll try again. Since Armory/Bitcoin-Qt wont work on my old PC, can I create a new "hot storage" wallet to receive my bitcoins without having to download the full blockchain? Can I think of a "wallet" as something that filters my personal transactions out of the entire blockchain rather than something I need to guarantee ownership? If so, then I can't lose any bitcoins by (at least temporarily) creating another wallet that "works". Right?
Your wallet contains your private key, which is what proves your ownership of your addresses. Without your private key, you can't spend your Bitcoins. If you create a new wallet in a different client, it won't affect your Armory wallet at all, but it also won't give you access to any of your old addresses.
To get at the Bitcoins attached to your Armory wallet, you'll have to get Armory running enough to export your private key. You can take that exported key and use it in another client, such as MultiBit or Electrum, or in an online wallet like Blockchain.info. If you can't even get Armory to export your key on your system, you can try taking the .wallet file and loading it into an install of Armory on another PC, then exporting there.