I'm paranoid about this and probably a little anal! As I see it, the critical elements in any backup scheme are:
(1) automation - you will forget / get complacent, so automate it!
(2) get something off site - while having two or more copies in your house / flat is great in case of drive failure, but when some sod robs you blind, that pretty stream at the end of your garden turns into a raging river or some higher deity decides its time to rain down fire from above on your abode, it's not going to help.
My own scheme is:
Main copy - Boot disk
Backup No. 1 - an Internal Disk
Backup No. 2 - External disk permanently attached to the Computer
Backup No. 3 - External portable disk stored away from the Computer, but not always
Backup No. 4 - Amazon S3 Cloud; offsite and allegedly highly redundant.
Backups No. 1,2 & 4 are on scheduled jobs, so it's not a case of remembering myself - that said these jobs balls up from time to time, so you do still need to check! Backup No. 3 depends on me remembering to grab the disk from it's hiding place in its waterproof Peli case, so is more ad-hoc.
All disks are replaced every couple of years for new ones and the old ones archived, so typically a full backup is permanently archived every 6 months or so.
I've ended up doing all this on standalone disks - I have used external RAID disks before, but the RAID controller board failed stuffing up one of the disks, so I decided to keep it simple. I also have a NAS lying around, again fully RAID redundant, but the thing is sooo slow on my network, I just gave up.
I don't know where you are based, but I have external hot plug connector and power kits for IDE / SATA drives of all physical sizes if you wanted to borrow them to try to get your current drive powered up correctly, but as others have said, if you suspect any physical damage to the drive, or the possibility of physical damage though use, stop and get it off to the experts. It's been around 5 years since I last had cause to use such a company, and it was around £300 for their services, but they got 90% plus back.