No - it's a whole different connector - narrower pin pitch than IDE. and
these are pins sticking directly out of the end of the case. I don't
know laptops, so I'm unsure whether this is a Toshiba proprietary
connection, or some kind of 'mini-IDE'.

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Laptop drives have a mini-ide which is very standard.

I have a USB drive adaptor which takes 3.5" IDE, 2.5" IDE and SATA drives, and I've done recovery jobs in the past. Feel free to give me a call if you like, 8551826 and I'll see what I can do.