Do you think a local PC shop will qualified to replace and reprogram a BIOS chip?  If a shop is qualified to do this, they should be able to find it for themselves. The chip's identity is probably printed on the motherboard next to it, so you can get your magnifier out and have a hunt. You'll still have to boot this PC up, even just to use it as a spare monitor. Seems like a lot of effort when you can get a stand-alone monitor. Sorry, but I think you're beating a dead horse...
I purchased this PC in hopes I could fix it.  I thought it was just about the black screen of death (which I am tackling), but I think there is another, what I believe, unrelated issue with the LCD screen. Yes, when trying to boot I get a black screen, but there is a dialog box about no HDMI input.  The right side of the dialog box looks OK the left is sort of distorted.  See below [IMAGE]   I tried plugging a Chromebox into the HDMI In and you can see the distortion extends across the entire left half of the screen [IMAGE] I don't want to sink a bunch of money in this old computer.  I this a common issue that can be fixed?    
XPS One 2710, poor image on half of screen