What would happen if I connect two different DC voltage sources in parallel?
First some theory:

In general, a PC power supply isn't expected to operate in a redundant mode (i.e. with outputs tied together).

In industry parlance, this function is called OR-ing (not O-ring). If a power supply is designed with OR-ing in mind, there will be several additions to the circuitry:


Some means of isolation (diodes or MOSFETs)
Some means of maintaining regulation at absolute zero load (anti-rollback)
Some means of load balancing (forced or droop)


These factors allow you to connect identical voltage rails together to provide load current beyond what a single supply can do, and allow for the rail to stay up (if the load can be delivered by N-1 units) if a single unit goes down. It also gives you some measure of protection if you accidentally connect a higher voltage to a lower voltage.

Also, most PC power supply returns are all tied to each other. There typically isn't an isolated output (independent return) available.

Now, the practical ramifications of your experiments:


Connecting the +12V and +5V rails together is only "safe" if there is some means of OR-ing on the +5V that can withstand the +12 applied to it. The +5V will not be delivering any current to the load, as it will be blocked by the OR-ing device.


Most likely you've back-biased the +5V and put 12V on some electrolytic capacitors that are probably only rated at 10V.


Connecting the +12V and +5V in series is only "safe" if one of those rails has a return independent of the other. If the returns are common, all you're doing is short-circuiting the rail that's on the "bottom" (the rail that has a return connected to the high side).


Batteries != power supplies. Energy going into a battery charges it. Energy going into the output of a power supply usually smokes it.