Start with a 6u flightcase of your choice. Add two 1u Supermicro servers, each with mirrored RAID drives. In the top two units, add a rackmount monitor drawer with a KVM switch - these are ludicrously expensive new, but you can pick them up quite cheaply used. At the bottom of the rack, fit a basic 1u UPS, just a few hundred VA worth in case you get unplugged. In the remaining unit, fit two half rack audio interfaces to the front and a little line mixer or a broadcast failover switch to the back.
Hmmm... I've just spent a week testing a custom setup for a firm looking for something like this. Managed to build a silent 3770 rig that can hold up to about 20TB of mechanical storage as well as a RME AIO into a 2U case.
I was thinking grab one of those slide out/pop up KVM draws and you can get the whole lot in a 3U case. Of course you lose the UPS unless you go for a 4U solution and you don't gain a physical line mixer althrough I was looking at using the RME mixer for that side of things.
Your other option is somthing like this http://www.overclockersclub.com/reviews/chieftec_bl01b/ where you can mount the screen to the case itself. Gigabyte also has something similer althrough in the past 12 months of trying to get them to import one to the UK I've still failed to get my mitts on one.
ScanProAudio & 3XS Audio Systems