You sure you can't get it out?
Not that that's relevant. What you posted will work exactly. What you probably should do is disconnect the power from the old hard drive and plug that into the new computer as well, but you probably don't need to. If you don't, the other computer will need to be on, otherwise the old hard drive won't be able to spin or send any data.
Just make sure the jumpers on both hard drives are set correctly. That might be a little hard to verify if you can't pull the old hard drive out, as it's usually written on top. If it doesn't work right the first time, I would bet nearly anything that it's a jumper setting - if you can't find a label that has them written, you may just have to play around with it.
Good luck!
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