Hi DJMetal
I'm not much help with fixing a seriously broken system. I usually have my data backed up then do a fresh install. If you need anything off the drive, password lists, bookmarks, your tunage

, get it off before you do a fresh install. If you can afford it pull the old drive, set it aside as a backup, and install on to a new drive, SSD if possible.
The recovery media usually costs extra, if a company closes its doors you likely can never restore a machine back to new including the applications. Hopefully this isn't a deal breaker, you should be able to install 8.1 fresh anyway. The only detail left to determine is can you download the drivers you'll need from Toshiba. I can't vouch for this dynabook website which comes up but it may be the source for your needed drivers. If there's an active Toshiba forum you might enquire there, maybe someone in here might know how to get the drivers, but you'll need the drivers for the audio, video, wifi, lan, etc.
I mention this as an option to keep this thing running, using the internet, email, listen to music, watch videos, simple stuff,
there's always a version of Linux - Ubuntu, Mint... and others. The truth is Linux would install pretty easy onto your oldish Toshiba, the question is, does Linux have everything you want in an OS, looks, apps. As far as getting your system back up and running I bet it would work fine. You should try it out even for fun, you don't have to install it, just boot to the media and run what is called Live, a little slower than a regular install but you can get an idea if it looks good for you, and if it detects all your hardware. A Live test really is an opportunity to try before you buy so to speak
If you do get a fresh install of 8.1 worked out, strait away create an image & recovery disk so you can easily reinstall later should you need/want to. Using Windows own tools does a good job, 2 USB drives is all you need to purchase - one for the image (bigger than the image), the other for the recovery drive (4GB should work) to install the image. There's videos on Youtube that walk the viewer through the process. Create the new image and recovery disk from a healthy OS in good working order otherwise why waste any time reinstalling a buggy OS. Most of us wait too long to create a good backup - after the system is degrading from use over time, a few too many MS updates that broke the system.
The product key is stored in the BIOS on your motherboard so what you do is download (for free) the ISO image from Microsoft, then use a free tool like Rufus (there's others too) and make a bootable USB drive from the downloaded image... or bootable DVD if you have a drive installed. I'm assuming you have a version of 8.1 Home installed, Pro might require other steps to obtain.
What you need to determine is the particular version of 8.1 installed, this ensures a simple reinstall... the correct OS will detect the key stored in the BIOS and wont ask you to type it in, the install will begin. If you are asked for the key you likely have the wrong OS on your bootable media. Also, you may need to activate the OS even after a successful install, I did, but activation should happen in a flash assuming working wifi and you're connected to the internet.
I downloaded the correct version of Windows 8.1 the first time

, I needed -> Windows 8.1 - English - 64-bit. I doubt you have the K or KN or the other versions. The worst is you need to reformat the media or burn a new DVD and download a different version, and try again. Regardless, you'll get an .iso image file about 4GB+ in size. Save it to a working computer that can be used to create the bootable media. If you have a USB port available I would use USB over DVD.
Here's where I downloaded my OS:
->
Download Windows 8.1 Disc Image (ISO File)
Here's the DynaBook site that seems to have some Toshiba drivers - I cannot vouche for this site so be careful:
->
Drivers & Software Support | Dynabook
Sorry for the long post, hope something in here helps
