XPS 8500, U2415, Sleep Mode issue

Hello,

I recently purchased a Dell U2415 monitor for a Dell XPS 8500 computer. The Dell XPS 8500 has a VGA port, but the new monitor does not connect by VGA. The monitor comes with a Mini-DP to DP cable, but the computer does not have a port for that. In searching the back of the computer, I found an HDMI port. I read online that the monitor could be connected HDMI to HDMI. I did so, but even after changing the display from DP to HDMI 1, it doesn't work. There is a message that says the monitor is in sleep mode. Hitting keys on the keyboard do not wake it up. I tried resetting the monitor by unplugging it, unplugging all cables, and pushing the power button for 30 seconds. No difference. I tried using the HDMI 2 port on the monitor. No luck. Same sleep mode message. I tried using different HDMI cables, no luck. The monitor won't come out of sleep mode. I do not have the USB 3.0 cable plugged into it as the instructions said not to do that yet. I am using Windows 10, and I checked that the monitor sleep mode was on NEVER. It still reverts to sleep mode. I'm not sure what else to try. I considered purchasing an DP to HDMI cable, but I'm afraid that I will have the sleep mode issue again? What cable will work with my machine and the monitor for the best results? Do I need a new video card? My old VGA monitor works fine on the computer, but I also read to not get a VGA adapter because the picture will not be good. I would like to utilize the HDMI port on my computer, if that is possible?

My computer:

Dell XPS 8500
Intel Core i5-3350P CPU @ 3.10GHz 3.10GHz
Windows 10 Home
64-bit operating system, x64-based processor

Thanks