First you didn't mention the Make & Model of your GPU card.
Also when the GPU card got physically shorted did the PC shutdown or kept going?
Most likely you burnt out and opened a thin metallic tracing at or near the GPU port where it shorted out.
Since your Warranty is voided due to Customer error, I would remove the GPU Covering and physically check to see if any metallic tracings are burnt or any electronic components.
Also check the Monitor's Cable for burned pins and at the GPU port. Also check the PCIe Power cable from the PSU to the GPU card for damage. When you remove the GPU card check the Motherboard's PCIe slot for damage.
You can always take it to a Computer Repair Center that repairs GPU cards but that will probably be expensive.
NOTE: depending on the GPU card you have you may need to replace the Thermal Pads besides the Thermal paste if you remove the Cowl or covering.
EDIT: Try uploading a photo of the area where the GPU Card got shorted out.
Hopefully if it is just one or two metallic tracings you can fix that yourself unless it is under a second or third layer of the PCB. In that case, it will be very difficult for you to fix it.
