Okay, it seems I have wired it up all wrong :lol:
LEDs are supposed to be in series, not in parallel. Back to Jaycar, to thank them for their lovely advice and heaps of stuff they sold me, and to get a completely different adapter, and more LEDs.
If you want info on how to properly wire up LEDs, this page is quite nice:
http://wolfstone.halloweenhost.com/Ligh ... gLEDs.html