I got around to finishing off the repair of the DVI/HDMI monitor and here it is re-assembled and running a test with the RaspberryPi computer. The RaspberryPi is temporarily in a simple Lego box to keep it from being damaged. The connecting HDMI-to-DVI-D video cable came out of DiscountNI of all places for just £2.99, which was a real result.
The small (and very tidy) power supply came out of an obsolete PC and I re-wired the mains input and removed all of the output connections before re-connecting one disk drive power cable with 2 Molex male connectors on it to provide 12v and 5v to the monitor.
At the monitor side, I stripped out the parts connecting the broken internal power supply to the main circuit board (mainly the isolating transformer) and re-cycled a Molex female connector from an old DVD drive as a power input connection. Some heat-shrink sleeving and couple of cable ties to neaten things up and the monitor is now running off the external power supply.
There are some advantages to this arrangement. The second Molex connector can supply a very healthy 5v to the RaspberryPi or alternatively the 12v supply could be used to run an obsolete laptop main-board via the battery connection. With a bit more soldering, 3.3v can be easily obtained from this power supply for running experiments using 3.3v ICs and communication modules.