The type of BSOD you're getting is of the 0x74 bug check - more specifically, BAD_SYSTEM_CONFIG_INFO (0x74).
The BAD_SYSTEM_CONFIG_INFO bug check occurs if the SYSTEM hive is corrupt. However, this corruption is usually unlikely, because the boot loader, known as NT Loader (NTLDR) in versions of Windows prior to Vista, checks a hive for corruption when it loads the hive.
This bug check can also occur if some critical registry keys and values are missing. Thee keys and values might be missing if a user manually edited the registry.
Unfortunately, this is a bug check that the only usual workaround is to do a clean install of Windows as there is no way to 'repair' a registry that is so corrupted that it leads to this bug check. The only other thing aside from a clean install that works (but usually never does) is attempting to load a Last Known Good Configuration via the Boot Options.
Regarding your questions:
1. The filesystem is corrupt and you cannot directly boot into the OS, however, if you have a secondary system such as a laptop or another desktop, you could hook up the HDD and use Windows Explorer (Start > My Computer > select the HDD) and manually back up any documents you want to keep. Do note you won't be able to simply drag and drop programs, as many programs install to the registry. You'll simply have to reinstall those.
2. You can use the same HDD. This doesn't appear to be a failed HDD, simply just the registry of your current OS installation is extremely corrupt beyond repair.
If and when you are comfortable and feel your issue has been solved, I'd recommend marking any posts of mine that answered your question as answered so this thread no longer shows up as requiring an answer.