Hi, I'll try to help with the problem here.
Aside from sending it to me for service I would ask some questions first.
1) Did you use it for the past 18 months with no problem, or did you not use it much and found the problem now that you are using it more?
2) It sounds to me like a power supply related problem. I see from your build notes your x0xi0 uses many
different LED's, most with a 220 ohms series resistor. This is quite a demand on the power supply. This problem will usually show up during start-up, when many LED's may be lit randomly, and the power supply isn't sufficient to supply this current at start-up. In this case the microcontroller never gets to reset properly and it doesn't boot up. The micro may also have brown out detection enabled which can make matters worse. The x0xi0's generally ship with a 9VAC/1A power supply, either US/Japan, UK type G, or Europlug type C, depending on where you live. This should be sufficient and I have never had a problem. First I would ask to take a picture of your power supply and post it here or email to me so I can see it.
3) From your comments it sounds like you can use the x0xb0x for a bit before it has problems. Is this correct? or does it get messed up right from start-up?
4) If not the 9VAC power supply itself, the problem is most definitely related to the 5V digital supply. I found the build notes for your x0xi0, including some pics. It looks like your x0xi0 was built into a x0xb0x that you had sent me. If you have a multimeter, the first thing I would do is check the 5V supply. Remove the back cover of the enclosure like in the pic. Try to keep everything else neat and assembled. Connect the positive lead to 5V as shown. Connection the negative lead to ground as shown (pin 2 of J4). The ground connection can be hooked up to any other ground point if more convenient. Turn on the x0xi0 and take note. The 5V supply should read 5V +/- 0.1V. Check to see if it remains constant at 5V. If ok at first keep monitoring while playing a pattern. When the x0xi0 starts to mess up take note again of the voltage. (click on pic below for large version).