What type of computer does that fit in, is it an HP slimline? It looks like a ATX small or Mini-ITX.
I don't think you will be able to find a power supply tester with these small connections they should all have the standard ATX connectors.
You could buy or make an adapter:
Edit: This is not the exact adapter that you need because it is a female to male and you need the reverse a male to female but it gives you the basic idea.
ebay
Here is a picture of one that someone made.
Edit: I'm not saying you should do this but it shows that the wires on both connectors may be the same.
A multimeter should tell if the PSU is dead but the PSU might just need resetting (Have the flea power drained).
To be tested properly the PSU should be under a load, not all power supply tester will put the PSU under a load.
Your connector looks like it has the same standard wire color code, this standard ATX info may help you.
Color Code Rail
Yellow +12V
Red +5V
Orange +3.3V
Black Ground / COM
White -5V
Blue -12V
Power Supply Voltage Tolerances
+3.3VDC, +5VDC, +5VSB and +12VDC 5% tolerances
-5VDC (if used) and -12VDC ± 10% tolerances
Green Power On / PS_ON#
When this green wire is grounded to a black wire it tells the the PSU that power should be delivered to the power rails (Turns your computer on, it is like pressing the power switch). When it is not grounded it tells the PSU not to deliver current to the rails (Your computer is off).
Gray Power Good / PWR_OK
The gray wire is called PWR_OK it’s a signal from the PSU to the motherboard stating the DC voltages are within normal ranges. It indicates that the +5VDC and +3.3VDC outputs are above the undervoltage thresholds of the power supply.
Purple +5V Standby / 5VSB
This purple wire gives 5 volts to the motherboard when it’s shut down, yet connected to a wall power outlet. This is why it is a good idea to unplug your computer when you work on the inside of it because it has 5 volts running into it and this 5V line is capable of delivering 2 Amps (Less than 1 Amp can kill you).
Standard 24 Pin connector
1. +3.3V
2. +3.3V
3. Ground
4. +5V
5. Ground
6. +5V
7. Ground
8. PWR_OK
9. +5VSB
10. +12V
11. +12V
12. +3.3V
13. +3.3V
14. -12V
15. Ground
16. PS_ON#
17. Ground
18. Ground
19. Ground
20. NC (Removed) -5V
21. +5V
22. +5V
23. +5V
24. Ground
