Testing continuity and voltage is test the basics first. In troubleshooting we're testing if there is power in and it is setup properly.
I hope you did not damage anything. If it was setup properly, you were able to use bios with atx psu, but not minibox, then likely is the mini box issue after we confirm it is set up properly.
UPDATE
As I've mentioned, I tested for continuity on the throwaway Pico and all was well. I tested the power brick and it too was reading the rated 12v fine. The £40 Pico plug wasn't showing the correct readings.
1. Using the expensive branded Pico plug, the system refused to power on.
2. I used the full ATX power supply to power it on and that went fine. BIOS was accessible. So I ordered a cheap £8 Pico as a test replacement for the £40 Pico.
3. Cheap Pico also fails to power on the mobo. So now I'm super confused. Did I receive two faulty Pico psus?
4. So i try again to power up the system using the full ATX power supply and this time the mobo smelt of smoke. No power or BIOS. I only did this second attempt in order to disable a 'cool and quiet' function that the AsRock bios has built in and enabled by default. The manual says leaving this enabled may cause PSU problems. I suspected this would be the problem that is failing both my Pico PSUs. Unfortunately, I could no longer access bios using the full ATX PSU as the mobo smelt like it got fried.
5. I've initiated a mobo RMA and ordered an Amazon same day delivery of the SAME mobo, make and model.
5. On arrival, I plugged in the throwaway £8 Pico plug and the system booted up instantly on first attempt! So I tried the more expensive branded Pico and it refused to boot.
6. It seems I must have had both a dodgy Pico psu AND a dodgy mobo all at the same time! Why else would none of the power supply units power it on, (except for that one time it did using the full ATX psu but failed on the second attempt)? How else do I explain that using a replacement mobo of the same make and model powers on flawlessly, using the previously tested 'failed' £8 Pico PSU?
Conclusion:
I can't say I have the answers. All I know is that the £8 Pico PSU showed me all the right readings using the multimeter and still failed to power on the first mobo. Replacement mobo powers on just fine using this cheap Pico. The £40 Pico does nothing.
Let me know if I can use this thread to ask you guys for some further help. I could really do with some more guidance. Thanks to 'the hack' for holding my hand so far.