Mictlantecuhtli said:
It won't turn on without memory.
It will turn on, but it will not POST.
If you have a too small powersupply the mainboard will turn off immediately; to prevent overloading the powersupply.
You
might see the fans trying to spin just barley and the diodes (if there are any) briefly flash...
It actually is possible to run a systems like yours on a 150w powersupply, but it needs to be more modern, providing enough current on the +5v and +12v lines, many old powersupplies that are around 150w simply provide power at the wrong place, i.e. more than enough on +5v but not enough on +12v...
This would be
an example of a really small PSU that might be able to power your computer, note that I by no means mean that you should buy such a powersupply, they serve very specific purposes you are not in need of...
When you get the new powersupply double-check all spacers under the mainboard, i.e. that they are in all locations where there are holes in the mainboard, and that by mistake there is not any on any wrong places, i.e. where there is not a corresponding hole in the mainboard. Most mainboards has 9 screw holes, in 3 rows. Some have an extra hole between the PCI slots to the left, look out for this one for example...