Ultimately, purchasing a new 16GB SSD for $17 on ebay solved the problem and now the machine is running perfectly!
I didn't use the exact same brand that was in there, because this other one was the cheapest. Here's the title of the ebay posting I purchased the part from:
16GB SSD Hard Drive LSS-16L6G-HP 735314-001 HP 14-Q010NR Genuine (A01)
In the computer the part is mounted on the motherboard and underneath the motherboard, as you'll see when following one of the already available guides.