I don't know much about making images of foreign filesystems on a PC but your plan may work, but it should also work directly through the emulator if the PC can even spin the drive up. To me it sounds like the problem is the drive is having trouble spinning up. These old hard drives tend to develop this problem as they age, and I have found that gently flicking the top of the drive with my finger while the Amiga is just starting up can make the drive start to spin properly. Think of an Amiga like the Millenium Falcon, sometimes you have to hit it a bit to get it to work, but it's so full of character and secrets that you'll love it forever.
Regardless of if you can get the old drive to boot or back up, you really shouldn't continue using the same old drive in the Amiga after this. These days there's no better option than a cheap IDE-CF adapter with a 4GB Compact Flash card instead of a hard drive. It's basically a solid-state drive so it boots faster and uses less power than a hard drive, and they're silent.
I'm not sure where you're from or what your budget is, but these few things shouldn't be too hard for you to get ahold of. It would really help if someone could send you a CF card with Workbench (and preferably ClassicWB or AmigaSYS installed on there also) so you could get started straight away, or at least send you a bootable floppy disk to start writing your own disks or installing things on your own drive.
I guess if you let us know where abouts you are from (or list it in your profile) we can help you with some links to local dealers or users where you can get what you need.
