We're all human and I think we've all lost data before. Right now at this moment, my backup situation isn't ideal.
I had an old SCSI 10K Seagate that after being stored had trouble spinning up. However, it did eventually start running again.
I also had a few IDE drives fail this way (while in an active machine), all at different times but all on the same PSU. That PSU was junk and may have contributed to the failures. I still have one of those drives and it seems to work again, years later.
In your case, I wonder if the motor has gotten weak and can't muster enough power to spin up anymore. The phrasing of your post makes it sound like it didn't get shut down very often, so when it did get shut down, the issue with restarting was a surprise.
Hopefully that's what the problem is. I think mechanical trouble with spinning up is one of the most recoverable situations you can have.
If it's spinning up but then shutting down because it can't find track 0 or something, that's a lot worse.
Assuming you're comfortable in linux:
I would hook up the drive externally to a linux box, with a fan nearby. If you can ever get it to spin up, use 'ddrescue' to start imaging it somewhere. It's designed for recovering an image from dodgy disks, and has some intelligence about how it does it. Read the man page, make sure you use the option to use a log file. ddrescue can resume the recovery in multiple sessions, and it will use the log file to keep track of which parts of the disk have already been recovered so it doesn't waste time (or mechanical stress) on anything redundant.
Sometimes having a fan to keep the drive cool will help it to keep running instead of locking up as it heats. That might not be an issue here but I'd prefer to have a fan ready in this situation.
Aggressive/risky:
Drives that struggle to spin up sometimes respond to being judiciously "tapped". Use your judgment.
This is risky, and kind of a weird idea that I've never actually tried before.
Assuming your problem is that the motor mechanically can't spin up the disk. If you think that's not the problem, then ignore.
But I wonder if providing a high voltage on the appropriate voltage line to the drive would help the motor to spin up the disk. You'd need to be handy with electronics and provide a separate, independent power supply to the drive that isn't going to anywhere else. Per ATX specs it can legally be up to 5% high, but this includes ripple, so to be within spec the reading you'd see on a multimeter would still be less than that.
If you actually attempt this, and have the means to adjust the voltage, then it's up to you how far to push it.
On a desktop drive I assume the motor would be driven from +12V, but I'm not sure if laptop drives use +12V. I don't remember.
If you still think it has any chance of starting up on it's own, or if you're considering professional recovery, then don't do anything that might hurt the drive.