This is what I was seeing...
According to the R-Pi Troubleshooting page...
Well the fix was easy then. My power supply was connected to a USB hub which then powered the RPi and the USB monitor, WiFi dongle, etc. Luckily I had an identical power supply as a spare. Plugging the other power supply let the photo frame start and boot normally. So problem fixed, but I wanted to know why it actually happened in the first place.
I checked the voltage output on both power supplies and it was pretty much the same and stable, so that wasn't it.
I didn't want to do any rewiring so didn't measure the current output, but this is what I suspected was going wrong. The power supply is a model WT0502000-MID which is rated at 5V 2A output.
I did a rough calculation of power requirements: 1A for the USB monitor (5W @ 5V according to specs), 150-300mA for the RPi (depending on load), 100mA for the WiFi dongle, 50mA for the USB storage. That's around 1.9A and is quite generous with actual values probably quite a lot less. Still this was close to the maximum output for the power supply. Still no problems, until I realised that I also had my RGB LED clock connected to the same USB hub as well.
The clock LEDs alone add around 6x 20mA of current draw, for a total of around 120mA, and this pushes the total current draw over the 2A maximum. Running it all like this for several months is what I believe caused the original power supply to stop working at it's peak output.
Lesson learned, lets see if the reduced current draw without the clock plugged in helps.