New OLED seems dead, how can I be sure?
The datasheet you have found is not for the same display. Yes, it's similar, and yes, it has the same actual OLED display unit on the board, but the PCB is different. So you cannot assume that the pinout is the same.

The fact that it's getting hot tells me that you have probably wired something wrong and you are injecting voltage into it somewhere where voltage doesn't want to be injected.

To find if an OLED is working you have to actively wire it up.  With an LCD you can just give it power and you should be able to see some visual indication that it's working (back light, some shadowing of the display matrix, etc). But with an OLED you can't do that.  An OLED is made up of a matrix of LEDs which are either on or off. By default they are off, and when they are off it's no different to there being no power. That's the big benefits of OLED displays - low power consumption and true black.

To get any kind of indication that the display works you both need to wire it 100% correctly and program the Arduino in the right way to actively drive it by displaying something on the screen.  My usual test program when working with a new screen is to simply print millis() in the top left corner.