How to disassemble my external hard drive

Ouch! Sorry to say thats not good. When a drive is running it is at its most sensitive point to be damaged.

When the drive is not powered (off) the head is parked in such a way as to not get damaged and/or damage the spinning platters. When powered the head is running across the platters like the needle of an old phonograph player.

In fact just like a phonograph player playing a record when you hit it, it will damage the recording on the disk (creating a scratch which causes the disk to skip). Here the heads are damaged first as they are more fragile but the platers can also get damaged when the head hits them damaging the information.

As to fixing this you would need watch maker skills and very specialized tools as well as a clean room. A clean room here is using very special air cleaners to filter the air so there is no dust. Even cleaner than what most operating room in a hospital have!

So the bottom line here is this is not something you want to dig into! So opening it up likely won't help here.

I assume you have important stuff on this drive and don't have a backup (as this was your backup).

If the drives power light is lighting then the disk is damaged and you'll need to think hard if you can recover what you need without the drive.

If you must salvage stuff then don't run the drive as its more likely going to damage it more. You'll need to ship the drive (case and all) to a data recovery service which has the needed clean room and skills.

What they do is open the drive up in the clean room and repair the drive long enough to copy off your data onto another drive. Then ship you back the new drive and your data. This will be expensive! but you have little choice at this point.