Monitor display problem

I'm currently using an HP 2159m monitor and it's works fine for when I'm just using my desktop. I just recently had to get rid of the TV that i had in my apartement so I've been left with only this, I tried hooking my 360 up to it and I'm having a bit of a problem where my monitor won't switch to the hdmi source while the DVI source is plugged in(my desktop), I try to just switch and it will just eventually get back to my desktops output, i switched the default and turned off auto switching as well nothing seems to work. It's confusing me because if i remove the DVI source and only my HDMI from my xbox is plugged in it works fine, I'd appreciate it greatly if you guys could help me with this problem, it gets a little annoying to have to unplug my desktop from the monitor everytime I will want to play my xbox on it.

Also I'm thinking about just buying another monitor instead of a TV is there any way other than paying a digital cable provider to get normal coax output from cable to switch to HDMI?