If the floppy is not it, one thing that may help is to get a Sandra report from your systems. Look for the Sandra information under the Windows General Troubleshooting link under "Help Us help you" up the top of this DUC web page.
Copy and paste the text output of the Sandra report (not a screenshot), it should look similar to the one here:
http://duc.avid.com/showthread.php?t=269583
--
BScout may have better ideas. I'm guessing he might have wanted to check you have an ASIO interface (you do, so great). But never assume Pro Tools has started up witt the correct interface. Open the Playback Engine dialog and check. Sometimes screwed up playback engines esp. ASIO4ALL drivers can cause weird hangs etc.
Just on that line of thought, and not that it should cause these problems, make sure Windows Sound and no other applications are trying to use the Apollo Twin, they should all be set to use the computers build-in audio.
You'll likely be removing all plugin files, trashing prefs again, checking Windows Event Viewer and other things if you still gave this behavior.