Are there any reasonable options for me for finding a replacement battery for an old Laptop?

[Cyber Akuma]

My mother asked me to help see if I can do anything about her laptop battery, since it instantly turns off if the AC adapter gets unplugged. 
 
Windows says that the battery is at 0% and not charging (Using the official AC adapter the laptop came with). Trying the trick where you delete and re-install the battery drivers didn't help, and when I tried to boot into the built-in BIOS diagnostics and run a battery test it said that the battery failed the test. 
 
Sounds like the battery is completely shot to me, problem is I don't seem to have any viable options for a replacement, especially one that won't cost an arm and a leg. 
 
HP's own parts site isn't even loading as of the time of this message, I have no idea how long it may have been down. 
 
The only 3rd party I could find that seems to carry OEM batteries (or so they claim) are Batteries+.... and they cost $90-100, a bit too much for us. 
 
Problem is, everywhere ELSE I tried to look had them for $15-30, which is suspiciously too cheap. And while most of the reviews are high (I wonder how many of them were just from someone who plugged in the battery, saw it worked for a day, and wrote a 5/5) if I tried to search for bad reviews I saw many mention it stops working after about 6 months.... which is something I see all the time with poor 3rd party replacement batteries. 
 
Honestly, when my previous old laptop's battery bit it I was never able to find a reasonable replacement either, but I didn't really look too hard, which is why I wanted to ask. Do I have any reasonable resources to try to get a replacement battery that isn't going to die in a few months and/or risk a fire without paying nearly a hundred for one? 
 
The laptop is a HP Notebook - 15-f162dx 
 
And the battery says to replace it with a model HP 776622-001

[Mindovermaster Moderator]

Go on eBay and buy one. I bought replacement bwatteries there all the time. Just be wary of the user. Make sure they have good selling rating, and their page looks apealing.

[goretsky Supervisor]

Hello,

 

The laptop model was released about six years ago, as I understand it.  It might be worth getting one of the inexpensive batteries, as @Mindovermaster noted, just to keep it running.  You can then save up for new laptop to replace it.  Be sure to back up any important data off of the laptop so that in case it does fail, you will still have copies of it available.

 

Regards,

 

Aryeh Goretsky