I was on my Mini last night, only 3-4 months old, practically new and it simply shut down. Screen went black, light went out and I have not since been able to get it turned back on. I have read a few instances of random shutdown from this board, but none of them seem to be my exact problem because everyone else was able to resolve their problem by plugging and unplugging and simple waiting. I, the next day, am still not able to use my computer. I just got back from being away for two days, the computer was shut off so I don't believe it to be an overheating issue. Could it be a faulty power cable? I welcome any thoughts. Thank you.
Since your mini is only 3-4 months old, if you are anywhere near an Apple Store, I'd suggest taking the Mini and power supply in and having the Genius Bar take a look at it. It is covered by a 1-year warranty.