Don't know Mac so the following is for a Windows PC and dependent on what resources you have available to use.
If you have a PC with a CPU that has integrated graphics, insert the GPU card and then check if the card is being detected in BIOS (if option is there) or in Device Manager.
If not there just verifying that you connected the power cable to the card?
If the CPU has no integrated graphics then connect a system speaker (example only) to the appropriate header pins on the motherboard (see mobo user manual for details) and check for any beep errors heard on startup e.g beep error code for no graphics adapter
If it is not being detected (or there is no appropriate beep error code heard) have you visually inspected the card (both sides) for any component damage? If it appears to be OK then you'll need to source the schematics to try and find out what's wrong. See Note below
If it is being detected, connect a monitor to each of the video output ports, one at a time to see if there is a video output on any one of them. If no good then you'll need to source the schematics to try and find out what's wrong. See Note below
Doing the above should at least let you know whether the problem is with the card "input" i.e. communication between the BIOS and the card is OK or not or the card "output".
You can also search online and find useful links like this which may also give you some ideas
Note: Be aware that there a several versions of the AMD Raedon HD7970 GPU card e.g. Asus, Gigabyte, Club3D just to name a few and there may be minor differences in the board layout, component values, circuitry etc to suit their requirements. The common factor is the GPU chip itself, so make sure that any info you find is relevant to the make of the card and not to the chip
Hopefully a start.
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