This forum post and this one have advice on which GPU to choose as compatible. You could try reseating the GPU but based on your information it is possible the card is bad. Just curious though, does the fan on the GPU run properly?

Re: Does this sound like a GPU that has gone bad

try remove the discrete gpu aka graphics card from your 8930 and connect video cable to onboard HDMI or DP video port.  If the discrete gpu is indeed bad, and the rest of pc is booting fine based on observation that router detects it connected to network, you ought to get normal video from onboard video port.

Re: If so, is there a GPU that I can buy and install that will fix this problem? 

yes and you can decide what to buy depending on what you need the gpu for.  If for 4k display only but not gaming, buy a simple gpu that supports 4k. If for gaming, many options and I would suggest take this opportunity to upgrade gpu above your current one if that has indeed gone bad.  Btw a loud fan noise could be from multiple sources.  If gpu fan was loud it suggests overheating.  When you test pc by removing the gpu, gpu fan noise should be gone.  If still hear it, the noise can be either cpu cooler or chassis fan.

Thank you for your reply.  

No logo shows up when I power on the system.  Nothing shows up at all.

I don't recall if a firmware update was installed unfortunately.  I have it setup to automatically install updates and that usually happens when my spouse uses the computer and he doesn't pay attention to the updates.

We haven't changed how we connect the display for over a year.  The monitor is a Dell S2240L.

Thanks.

Thank you.  I will try your suggestions (possibly not today though) and advise on how it goes.

I actually opened up the computer today and discovered that there is nothing in the  PCI-Express x16 card slot.  Does that mean that the onboard video port has gone bad and that I need to install a gpu into the PCI-Express x16 card slot?  (as I mentioned, I'm not too technical and I'm about to give up and contact Dell or Best Buy because I don't want to )

It would be a good idea to take it to Best Buy Geek squad for an opinion.

since you do not see any discrete gpu inside pc, it shows you have always used onboard video port before which was working until recently.  It can be due to a corrupted bios or other thing wrong w motherboard.  You do not need to get a discrete video card to help diagnosis or repair now.  What this forum often recommends to users in this situation could be over technical, but if you are interested in knowing some of them just for discussion not necessarily doing it yourself, first unplug power from pc, press power button for 30 sec to drain power, replace cmos battery with a new battery CR2032 ($1-2), clear cmos settings by moving motherboard jumper pins, and if still no video, attempt a Dell bios recovery.  The last three steps mentioned can be a bit technical I admit.

I did the steps regarding replacing the CMOS battery and unfortunately it didn't work.  I could see lights lighting up and heard the computer doing its thing but still no signal to the monitor.  I will bring it to someone to diagnose it in a few days.