I'm really happy to read this, because I have exactly the same problem and getting very frustrated with this issue. Sometime I can power on the DX120 without no problems, but very often I cannot turn the DAP on at all. The backlight is switched on for few seconds and after this the unit gets powered off. Because of this issue the DX120 is still unusable for me.
What about the Batch/Factory Tool that Paul recommended? Did that help you with the problem??
I use firmware 2.2.42 and I have the problem is usually after loading the battery or otherwise when I powered it off over the night (for 6-8 hours).
Any help is much appreciated!