Understood: Silverstone Essential Series 500w (model: ST50F-ES230). FYI: There was version 1 and 2. They have 34A and 38A available on the V12 rail respectively.
Please do the following:
Step 1 & 2: Update motherboard BIOS / chipset
Latest versions are [F7] date: 2015/08/11 AND [11.0.0.1158] date: 2015/09/17 respectively
http://www.gigabyte.us/Motherboard/GA-H81M-HD3-rev-10#support-dl
Step 3: Use a different PCIe cable from the power supply, in case cable or cable capacitor is malfunctioning.
Step 4: Call Gigabyte support and inquire if the 1050 Ti is compatible with your motherboard. I'm confident that they would know the absolute answer to that question. I tried to contact them on behalf of your issue but they are closed on the weekend: Gigabyte (626) 854-9338; M-F 8:30 am - 5:30 pm PST
Step 5: Try your 1050 Ti in a friend's computer and determine if the usage is normal.
Step 6: Submit a RMA from the vendor ASAP. This is just so you have the option of returning the card for a refund or exchange, if you can't resolve this problem. Hopefully you purchased it from Amazon, NewEgg or somewhere with a no-hassle return policy.
By the way, I checked both NewEgg and Amazon customer reviews for the Gigabyte GA-H81M-HD3. The 1050 Ti released in October of 2016. On NewEgg, out of 51 total reviews, they were all from July 2016, therefore none were relevant. On Amazon, there were only 58 reviews. Of those, only 5 were published starting in July 2016 and none of them mentioned the 1050 Ti or any other Pascal card.