That sounds like it might be a different problem than I had - as in my case, when my machine ostensibly died, I could still plug in an external monitor/keyboard/mouse and use it. In my case, the input cover would die - the power light would be off too, but the computer itself was running.
Regarding updating the SSD firmware, it was pretty complex. Start by reading this thread:
Don’t give up hope!
After understanding the issue as described in the thread, I used the script here (note: it’s been moved, but read it and follow instructions anyway):