Windows 8 Whether and which preinstalled os do i have?

Does this laptop still have the hidden recovery partition showing in disk management? If so you could use that to reinstall the OS to factory condition (like new - day it was originally opened). See here....starting with page 60 of the manual.
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In Disk Management there's only the usual 'C' drive (and 'System Reserved' 100MB), but it's only about 212GB of what was supposed to be a 250GB SSD drive, as if more than 30GB was somehow hidden or missing. Is it possible the recovery partition is there but doesn't show up in the manager?

If it's not showing in disc manager, it's not there...which means someone clean install of an OS that wasn't the original OS. You can use this link and follow instructions on how to create a windows 8 ISO and then use the OEM windows key you found in the BIOS to install windows 8/8.1 Pro. You may have to call MS for a phone activation.....no biggy as it's pretty easy and quick.

http://windows.microsoft.com/en-us/windows-8/create-reset-refresh-media

https://support.microsoft.com/en-us/kb/950929

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Which OEM key do you mean? The one retrieved in PowerShell via get_win8key.exe? Even then how do I know whether to install Win 8/8.1 Pro/NoPro N/noN? Do I understand correctly that if I happen to install version matching with one that was presumably originally installed, it should detect the license and not ask about the key?

Hard to say as that model has both 7/8 for an OS....you'll need to contact Lenovo directly and see what they have to say.

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Is there anything on the back of the laptop....the COA sticker saying what version/bit type it came with. Generally on the newer laptops it's in the battery compartment.

I'm kind of confused whether your Mom bought the laptop for you to use, or she bought it and it doesn't work right and she's having you fix it for her to use??

Either way, this is a common ploy that unreputable sellers do to get an unreasonably low price on a laptop that normally costs hundreds of dollars. Chances are, if she paid less than $100 for a Windows8.1 laptop, it's got pirated Windows software on it.

Bass gave you some ideas on how to fix it; but it's not something you should even have to deal with on a legit laptop purchase. Some questions for your Mom. If she bought it online, where online? was it ebay? Amazon? exactly where?
If she bought it from a legit seller on ebay or Amazon, she needs to return it for repair/replacement or refund. This is usually pretty easy if it's an online retailer such as Best Buy, Staples, Tiger Direct, Newegg, etc. Of course, they don't sell laptops with pirated Windows, so it's more likely she got it from a much smaller independent reseller with an online store. In that case, she should attempt to return it for one with legit Win8.1 software or a refund. Most smaller resellers, such as people with ebay or Amazon stores will do this no questions asked. If however, you bought it from an individual seller, with no dedicated online store presence, it's most likely a scammer, which you'll know if your Mom tells you their listing or ad says "Laptop Sold AS-IS condition" or similar wording. Additionally, if their listing says "ABSOLUTELY NO REFUNDS!" or similar, that's another sign it was purchased from a scammer. And what's worse, people who sell computers like that are often selling stolen property, as it was stolen from someone's home or office in a burglary. Sometimes, the person who physically stole the laptop, tried to disguise it from being stolen by installing a pirated copy of Windows onto the legit copy it came with to hide the fact it was stolen. Chances are good that if she indeed has the name of the company she bought it from, and I haven't heard of it, it's probably stolen. Often, people who steal laptops use a "fence" which are individuals who then sell off the stolen property at ridiculously low prices online. It could be a "fence" that your Mom bought this laptop from, not a legit e-commerce store.

Will wait for you to post back more information, but if she got it from a legit store, especially one who is a Microsoft Platinum Partner reseller *see the stores I list above*, they would accept the return and put a legit copy of Win8.1 on there and return it to you for just 1-way shipping cost, or offer your Mom a full refund. In this case, you can get it fixed for less than $50 US. Of course, if she paid less than $50, well, keep reading.

If it's one of the other "iffy" scenarios, you'll find out pretty quickly if you try to return it to the seller she purchased it from. In this case, if you don't find a COA LICENSE KEY that Bass mentioned that looks similar to this file. If this COA KEY was removed from the laptop, it's another indicator it was probably stolen property, and she was duped into buying it. Personally, I would either turn that laptop into your local Police Department, or recycle it at your local landfile where they melt it down. If that laptop was used in committing a crime, it can now be traced back to you once you go online with it.

Word to wise.
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