Unable to partition internal Toshiba drive for OS X re-installation, Trying to resurrect an older MBP and I'm at my wit's end on how to go about it. Hoping you all might be able to shed a helpful light on things.

The MBP in question is circa 2012 and immediately boots to the OS X Base System on startup. When going through the 'Reinstall Max OSX' option (High Sierra, in this instance) I'm able to proceed past the license agreement but lack any disk volumes besides the Base System (which I clearly can't override). Additionally, the base system itself seems to take up roughly 350 GB of the total 500 GB hard drive. 

When moving through Disk Utility options I am only able to run a First Aid check or Partition both the OS X Base System and the internal Hard Drive (a Toshiba MK5065GSXF HDD). When attempting to partition I have no option to increase the number of partitions. Additionally, the OS X Base System now registers as being 500 GB in size in this menu. 

So,long story short--the hard drive seems borked. If anyone has any ideas on what I might try next, I'm all ears. Otherwise, this little dinosaur may end up being recycled.
Don't let that poor dinosaur extinct yet.
Now I'm sorry but I'm not sure what you are referring to with 'base system' that's taking up 350GB. Assuming that it's the recovery partition, was that already in the drive? It sounds like partition map is broken. 
If you are willing to wipe that hard drive clean, there are few things you can try.
Erase the disk using terminal in recovery mode and run verifyDisk and repairDisk. If this works then you could probably just create new osx extended partition to install osx. 
If partition map is broken, you could use external computer to repair them using third party software. 
And since you mentioned that it's a MBP from around 2012, does it have an optical bay? if your model is the ones before retina screens, there is a high chance of broken SATA cable. It is a known issue with MBP from those times, and it breaks quite often, leading to very confusing hard drive problems. If possible check if hard drive works fine on other computers and if they do, it is likely that it's your SATA cable.