HDMI port broken leading to other graphic problems x51

Yesterday when loading up my x51 the screen went black and it said no hdmi signal could be found. I assumed the port had just broken but when i swapped hmdi port and turned my pc back on it said that my pc had recovered from an unexpected error. Now every time I try to use the broken hdmi port my pc shuts itself down, now this wouldnt be a problem but i can no longer run anything other than low quality graphics on any of my games, so im thinking there may be a bigger problem. Does anybody have any ideas how to fix it?

Two days ago whilst loading up my PC it shut down and said no HDMI signal. I assumed it was just it was just a broken HDMI port so I proceeded to swap to the back up HDMI port. But now when I try to play game that my graphics card can clearly optimise it struggles to run any game even in low quality. I opened up my GeForce control panel and it now says that it can not optimise games on this PC due to lack of GPU which makes me think my Graphics Card has bust as part of the HDMI problem (if I use that HDMI port it works for around 1 minute before it shuts down my PC and then says it recovered from an error). Any idea of what the problem is or how to fix it? Or should I phone up Dell to get it fixed as my PC is still within warranty.