The single beep could mean that the CPU fan has failed and the beep is telling you that the MBs thermal sensor has shut down the system to prevent the CPU from frying or that you have a Ram or a video chip/card problem.
Testing a PSU with a multimeter is not conclusive as the PSU is not under load like it is when it has to supply all of the computers hardware, see my canned text below;
As a PSU puts out various voltages +3.3V, +5V and +12V it may appear that the PSU is working correctly but it is not, any significant drop of any output can prevent the system from booting up, the other scenario is a significant increase in the output which can be worse as it can fry one or more major components such as the MB, CPU, Ram, add on video card etc.
Please be aware that there are no user replaceable parts in a PSU so a bad one should be disposed of in a responsible manner and any type of conclusive testing will need to be done by a suitably trained Tech who has the required testing equipment and the relevant knowledge as to how to use it.
The +12V rail is only marginally low but that may change dramatically when the PSU is under load.
Do you have an add on video card or are you using the MBs integrated video chip.
How many sticks of Ram are fitted.