The paperclip test only indicates that the +5Vstandby portion of the PSU works and that the +12V works at least partially. You really need to measure the positive voltages with a meter, preferrably a digital one (Harbor Freight cheapos are perfectly good for this). Do not rely on a PSU tester that merely turns on LEDs because they'll light up even for voltages that are 20% too low. A PSU tester with a digital readout is fine but costs more than a multimeter and is a lot less versatile. However it's best to measure under realistic loads, but even that won't always indicate problems because meters can't read fast changes, including ripple.
Try another PSU, preferrably without buying one.
Originally Posted by jak
I have a feeling it could be my RAM because recently the casing that cover the actual memory stick came off so I thought maybe there might be damage to the RAM but I'm not sure if this would cause the computer to not boot at all?
That cover is called the "heat spreader" or, more correctly, the "purely decorative and useless heatsink". If it simply fell off, without force, there's probably no damage, and you can safely leave it off. But if it got knocked around it's possible a chip was partially pulled off as well, causing one of the solder joints under a chip to break. Sometimes you can check for this by clamping each chip with a clothes pin (spring type, not slip-on type) while the AC power cord is unplugged (so no +5Vstandby power is fed to the motherboard -- it powers the memory in standby mode), and any change in the problem indicates a broken solder joint. Your memory is probably warranted for life.