Explain more about your question… Most Mac Pro' machines can take a SSD drive upgrade if they are not already SSD. The latest OS at this time is Mojave, which is available to machines made late 2012 or after and is free. Earlier machines can enjoy High Sierra also for free.
You have a lot of testing to do still before hanging this great little machine up. What drive is in it -HDD or SSD? Have you tried isolating the RAM one stick at a time? Have you formatted the drive and reinstalled the OS? You said “hold all keys down continuously” or it shuts down. Can you elaborate ? This for safe mode boot, just shift? Internet Recovery mode work?