Hard Drive Failure? Cannot run CHKDSK. Recovery?
You do not mention many symptoms, so it's hard to say what the issue is.
First of all "this transfer rate will simply not do" is irrelevant. When a drive is dying any moment that you have access to it should be used to copy your data off. Consider yourself lucky that it comes alive one more time instead of complaining about the transfer speed. Leave it on, don't reboot, and keep copying your data off it, even if it takes weeks. That is the first thing you should do. Even having run chkdsk was a bad idea.
If your drive is not making clicking noises I suspect the drive surface. The procedure I recommend in these cases is:
1) Do not shut down/reboot any more than necessary. If the bad spots are in critical sectors at the beginning of the disk the system may not boot up again. Write processes on shut down/reboot may also worsen the situation.
2) Avoid writing to the disk. Pulling it out of your computer and putting it in another computer as a non-primary disk is a good way to prevent software (the OS) from automatically writing to it. You already tried that.
3) Optionally, try to make an image of the entire disk or in one way or another pull all the important data from the disk. There's lots of variations on how you can do this, but whatever method you choose, read only!. You're doing that now.
4) Run software that will check for and fix bad sectors.
In ascending order of thoroughness (which generally also indicates the time they will take to run) I recommend:
Run Seatools for DOS (not the Windows version; download the ISO), and choose the 'LONG Test'. This program is free.
Run HDD Regenerator. This program is not free ($99 US).
Run SpinRite (running the executable under Windows will extract an ISO that you can burn). Choose level 4 for thorough testing. This program is not free ($89 US) and is the only one that I know that can often recover data from damaged sectors; this may take a long time though. It comes with a money-back guarantee.
All three programs scan the hard disk at the physical level, and should be run from a bootable CD. They don't care what OS file system is being used.
5) Finally run software that does logical checks on the disk structure, like chkdsk. This could very well not find any errors after step 4.
Added 21 feb 2014:
1) People often have the tendency to do step 5 before 4: chkdsk is at hand so why not use it quickly. This is not optimal. If the disk sectors are bad and this leads to corrupted file allocation structures, tools like chkdsk will do their best to fix the logical file structure. What they fix here is irreversible. They will generally not be able to recover everything. If you first do step 4 and it's just a matter of damaged physical sectors, those kind of programs may well be able to revive or reallocate the bad sectors and keep their data. If that happens the OS will no longer have problems with the file allocation structures and all the associated logical data structures will be fine (that's why I wrote "This could very well not find any errors").
2) You may not have a spare disk at hand or may not be able to read from the damaged disk to do step 3. That's OK, step 3 is just a generic precaution: "Before you start doing anything irreversible (steps 4 and 5) try to get as much data off as possible".