PCIe slot is rated to 75 watts maximum. In fact there is quite a bit of headroom, each pin is rated for 1.5A continuous and 2.5A peak with an acceptable temperature rise. Same rating is applicable for all slots from PCIe 1x to 16x, only some of the first 18 pins are used for power. We used this to build a 30-channel modular amplifier for a client and we used the PCIe connector (obviously with a different pinout) to supply the power, signal and get the speaker output from a single backplane. There are 5 +12V pins and 7 ground pins in a default x1 slot, at 1.5A each that's about 90 watts from the 12V rail alone. Then there are more 3.3V pins.
The 75W limit is set by PCI-SIG and is not the limit of the connector surface. Motherboard manufaturers only need respect the PCI-SIG spec to pass certification and market their boards. On the GPU side, thigns get complicated. While most cards are limited to run 50-65 watts from the slot, depending on how the rails are wired it is entriely possible that they draw too much current from the rail for an instant. For cards that conflate all their supply rails into a single large rail, this could cause the card to lean harder on the slot power than the incoming +12V power connector. Typically this is rare, as the slot rails are directed specifically to the board logic and some of the minor auxiliary circuitry. It may also be used to power the VRM chips (not the VRM itself, just the chips) and sometimes the front end video encoders.
To the burn, if you had it at power on it's most likely overvoltage - a brief surge that caused the regulation to fail before cutting out the output voltage. Not vetting the build thoroughly after getting a smoke signal, and then proceeding to power on again was the death warrant, if the first power on didn't kill it the second one surely did. This was a hardware failure, it sucks, but what's done is done.
There is an outside chance that the card is OK. It may be just a trace failure along with whatever else vaporised instantly. Motherboard is likely unrecoverable. The depth of repair needed may be just too high, because motherboards tend to bury power layers and if soemthing there opened p you won't be able to get to the layer. GPUs still run most of their power up top and bottom, so even vaprosed tracks can be (mostly, but not always) fixed. There are guys who advertise PCB evel repairs on GPUs. I would hesitate using their services.
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