XBOX NOT CONNECTING THROUGH DISPLAY PORT OR DVI ADAPTER

Now I know this may be a common problem, but I've been ALL over the internet searching for an answer and I just can't find one. This is my last resort, anything will help. Let me explain, SO it started off with me wanting to hook
my xbox up to my 2nd monitor (HP Compaq L2206tm) which I understand does not have an HDMI port, as I use these 2 monitors with my pc using adapters, spliters, etc. I know these monitors aren't necessarily meant for gaming but I got them for a pretty good deal
so I couldn't resist. Along with the story, so I finally end up grabing my HDMI cord and xbox one and plug it into the dvi adapter (I don't know exactly what it is, but it looks like a male DVI with a spot for an hdmi cable). Basically I plug my xbox in, expecting
it to work, and I get a big message from my monitor saying that theres no input and it shutting down to sleep. After repetitively trying everything to get this to work by doing hours of research, I gave up and decided to aproach it from a different way. Theres
3 ports on my monitor, a dvi port, vga port, and DP port (display port). Assuming the display port would work better due to it being newer, I ordered an HDMI to DP cable thats like an all in one cable. So I get back from BestBuy, excited, and unbox the cable.
I plug it into my xbox and directly into my monitor ANDDDDDDD nothing... Well actually this time it did register that something had been plugged in but it didnt show it connected to anything. Im tired of researching this and am starting to assume its just
my monitor, seen as it ended prduction in late 2015 and they are kinda old. Can someone help me figure out the problem? And just an extra thing, my xbox is set to the same hz and resolution as recommended for the monitor. So should I sell these and buy a newer
model monitor or is it a problem with my xbox? Like I siad, anything will help! Thank you!

:)