My boot drive on my PC is dying. How do I save the programs quickly?

I heard the awful grinding start this morning, so I shut my PC down.

Unfortunately, it’s the C drive with the OS and all my programs installed that’s dying; I’ve had this PC for 8 years and I don’t have all the passwords for everything. Is there a way I can clone the C drive onto another drive quickly and swap boot drives? I need this PC in order to do a great deal of work, so any help I can get ASAP would be appreciated.