The same thing is happening to my Solidoodle 4, I cant heat the nozzle and bed at the same time because repetier crashes. Also, when I try to manually control the printer, the Z axis moves in the oppsoute direction. When I hit Z+ it goes down and Z- goes up, thats weird, right?

If I was in your position again, I'd consider returning the PSU just so I had a working stock one, but I'd save the wait and order a new one myself on the side. Get a little 12V 300W PSU off of Amazon for <$50, some 2.5mm jacks (check the page for exact barrel dimensions - I forget) <$5, a surface-mount fuse panel (~$5) for the 12v outputs, and a fused plug with built-in switch (the kind of plug that a computer power cord plugs into) for the input ~$6. Wire it all up, design and print some mounts for it to mount nicely on the back of the printer. Then you're golden, especially if you want to do any future upgrades (more fans, LEDs, RaspberryPi host, etc).

The same thing is happening to my Solidoodle 4, I cant heat the nozzle and bed at the same time because repetier crashes. Also, when I try to manually control the printer, the Z axis moves in the oppsoute direction. When I hit Z+ it goes down and Z- goes up, thats weird, right?

Actually the Z axis thing is typical because it is based off of where the extruder is, not the platform.  Imagine the platform as being a fixed location and the extruder moving up and down and it makes sense.  Unfortunately, not sure why nozzle and bed aren't heating up together.

Careful with those ATX box power ratings - they're a sum of all the rails (3.3, 5, 12, -12V usually). The 450W supplies I tend to find lying around usually do only about 18A (216W) on a single 12V rail - which is still an improvement over the 12.5A rating of the SD3/4 supply. Also, make sure you load up the 5V rail to about 5W (I use a 4.7ohm 10W wirewound resistor) to improve regulation (reduce droop) from the 12V rail - these things are cross-regulated. If you don't do it, it will have much worse droop than the stock supply! Also, although ATX supplies are supposed to have a maximum noise level, it's pretty generous and it's expected that quite a lot of power filtering happens on the motherboard (that's what most of those capacitors are for). I'm getting close to using one myself, as I can power my raspberry pi print server off the free 5V!

Now, I haven't read the datasheet for the main microcontroller, but as I don't see any LM780x chips on the board, I will assume it runs at 12v. Which means its "brown-out" condition is probably around 11.3v. For a cheap power supply to try and meet the current rushes of the heaters with an unreliable power source itself, a 0.7v drop is borderline expected. IMHO, the person who designed the PCB should have put a 10uF electro. and 1uF ceramic cap on the chip's input so the chip would be immune to such inadequacies. In reality, if I ever have trouble again, I will just swap right over to a computer PSU. 400W minimum and far better current-draw response.

For anyone reading in future - the constant machine "crashing" was due to a bad power supply. Also, the new power supply sent to me ONLY works when hooked to a UPS - apparently my wall outlet power isn't good enough.

That sounds shady. Much more likely the replacement power supply has electrical issues than the wall outlet.  Especially if you try another section of your house.

Some of these cheap power supplies cause crazy noise fed back into the outlets. I don't really understand how it works.

UPS would somehow be isolating the problems.

For anyone reading in future - the constant machine "crashing" was due to a bad power supply. Also, the new power supply sent to me ONLY works when hooked to a UPS - apparently my wall outlet power isn't good enough.

That sounds shady. Much more likely the replacement power supply has electrical issues than the wall outlet.  Especially if you try another section of your house.

Some of these cheap power supplies cause crazy noise fed back into the outlets. I don't really understand how it works.

I swear this board is faulty. There is no way a communications problem this repeatable across multiple PCs has to do with anything else...

EDIT: Also note that the bed does continue heating after locking up.