So was it correctly connecting/ synchronising and then one day just stopped ?
If so, then it could be something unusual on your network with the port (8333) that MultiBit HD uses to connect to the Bitcoin network.
The fact that you can use another machine on the same network is odd.
One thing you could try is to install Lighthouse, which is also bitcoinj based and connects to the Bitcoin network on the same port.
http://www.vinumeris.com/lighthouseIf that does not work then it suggests that Bitcoin network traffic (on port 8333) is not successfully getting to and from your machine.
If you cannot get traffic on that port then yes I think you will have to restore your wallet elsewhere and move the bitcoin.
For an alternative Mac client I obviously mainly use MultiBit HD but also use Electrum and Copay and both are good wallets.