Hard drive not recognized by laptop, No bootable device.

Hard drive (500gb) is not recognized in the Windows 7 laptop (daughter's) . I do see it in the Bios.
I removed it, plugged it in externally to another laptop (my windows 10) via encloser case, and it's not recognized there either.

The hard drive is NOT making bad noises. I hear it spin up. I've tried
Troubleshooting in different ways. I would like to try to save the hard drive files & info (including the Win 7 OS) if possible without having to spend money to do so.

I have a spare 120gb HD that has ubuntu 18.04 that I inserted to the LT, so that's good.
But I'd like to get win 7 back.

So here's my questions.
1) Can I reinstall her Windows 7 back to a new clean hard drive?
It came pre-installed on her LTop. There is NO cd disk of it. ☹

2) If yes, where Can I find the product key, or whatever it's called, to authenticate
Win 7 at installation? Stickers are on her LTop bottom.
3) If I can do this, where can I go to get the download?

Of course having made a recovery disk when she purchased her LTop 5 yrs ago, would have
Been the thing to do, but it didn't happen.
Please help, I thank you in advance.
*Gateway Windows 7 home premium laptop

To be more specific, I placed HD back in the unit to explain what i see in BIOS.
In bios (information tab): HD toshiba mk5059gsxp... It shows is HD there, however it does not show the capacity.
When i start pc, it goes to:
Pxe-e61: media test failure, check cable.
Pxe-M0f: exciting Broadcom pxe rom.
No bootable device-- insert boot disk & press any key.

I took it out, then connected it to MY laptop via external enclosure case, and my computer does not recognize it either. However, in Disk Management I see it there but it says unallocated and is labeled Disk 1 unknown. I right click on properties, & box says is working properly, lol. Right clicking only gave me 2 options (properties, & help) because everything else is grayed out. I think the only way it'll let me do something is if it gets formatted at that point.
Thank you for your reply. What do you advise?

I tried Recuva and it didnt even "see' the bad hard drive, and I scanned with easeus and nothing.
I did install a few others you mentioned but was not sure I wanted to "risk" using them.

So....
The sticker my daughters Laptop has her product key. It is 25 characters long.
I think she might be ok with my wiping out her hard drive and reinstall back Windows .
On the Microsoft site, there is a place that will let you enter the product key to do the download for free.
.
(1) Which disk repair utility do you recommend I use to try to prepare her "bad" HD for the re-installation of Windows 7 home premium (64 bit) on her same Hard drive?. I will assume it still has some life in it.

(2)Should I download & save the files to MY working laptop, then use Universal USB installer so that it can be copied to a USB flash drive. Then boot up HER laptop to install via USB flash drive and proceed with the installation?

(3) Will it go like mentioned, or will Windows prevent me from installing even though I have the legal product key?

(4) Should I not risk doing the installation to her "bad" HD in case it fails? I guess she should invest in another HD, but for now maybe try to test the original HD again to see if it works. That is why I ask what can be done to prepare the HD. At that point, I may be able to tell if its useable or not prior to windows installation.

Thank you for your help.

[ATTACH][/ATTACH]Thank you for your inputs & great advice, Mega & SIW. I've been at this for a longgggg time now. Come to accept I did not use her disk, but instead, used my spare 120gb HD (I know, it's small ) but at least if I mess something up, it will be better than messing up something bigger or newer.

Here's where I'm at:
I got Windows 7 home premium 64 bit sp1 installed!!.

Upon set up, it allowed me to" skip " the part to enter the 25 character product key. Reason i skipped, was just in case i do another install to a larger drive for this same LT, & i redo this all over again; Maybe had i entered the P.key, i can only use that P.key once?? Just my thought....

Most everything is ok so far EXCEPT for drivers under "other devices" in Dev Manager.
I uninstalled/ reinstalled & nothing. See above photo.
I can't connect to Wi-Fi to see if I can update/ upload drivers (prob cause of this problem).
Should I try via Ethernet cable.?

If that's the way, is there a simple way? I can also Google it if you're all too busy to reply.
Note when I had Ubuntu installed on this same disk, everything worked fine including the Wi-Fi. There is no trace of Ubuntu on this disk. Installation went fine in that area.

Please advise,
I Thank you kindlyby

Instead of taking pictures, use the snipping toll to generate the images (%windir%\system32\SnippingTool.exe)

- You can use the COA key only on one computer, as many times is required, but if you do it more than once in 6 months it may ask to activate by phone. So don't activate till you're done all installations.
- You can install everything on the 120G HDD and then clone it to a bigger HDD.
- Use this tutorial to find the hardware specs. We need them to find the proper drivers. System Info - See Your System Specs - Windows 7 Help Forums
- Go to the Gateway site and see if they have the drivers for the laptop.
- Meanwhile, set Windows updates to manual (under services) and never check on WU page. On your computer download SP2 and the security only updates - MS releases SP2 for Windows 7 - Windows 7 Help Forums