First thing to do is check SDM. It's running by default, will still run if the panel is in service mode, and only a dip-**** would turn it off in the project. 99.9% chance it's turned on and if there is any life in that panel, it will be running. Just connect to the panel with a laptop and go to WhateverItsIPaddessIs/sdm in any browser and is should give you a full rundown of what's going on. If SDM isn't working, then it isn't just the screen.
It's common practice to make the visualization available on a VNC server also since B&R makes it so easy (literally takes 10 seconds to mirror the HMI to a VNC server, so most B&R guys do it automatically). If SDM is working and reporting the panel is in run mode, you have a fighting chance that there is a VNC server with your HMI. Any viewer will work, I like RealVNC's viewer. The default port is 5900, which is the standard VNC default port. If asked for a password, the B&R guys like to use 'v' for view only and 'c' for view and control (so just use the single letter 'c' as the password).
If SDM is working but not VNC, I'm sure the machine builder would be willing to add the VNC feature for you if they didn't to begin with and send you a CF card image you can burn to your CF card using any reader and the free Runtime Utility Center software from B&R. Even easier if you have an **** or something they can use to do a remote download. Before you reburn a CF card, you might want to ask how they store your recipes. Usually, they can be recovered via FTP from the user partition (F:\), so you can save them before reburning the card. If not, you can get fancy and use Runtime Utility Center to upload the recipe structure and save it to a text file and then download it again after you burn the CF card. Be sure to let the OEM know that you don't have Automation Studio because if your panel is out of warranty, then it was probably programmed in an older version of AS and they'll either have to update the project to a newer version (easy and low risk) or jump through a bunch of hoops installing the older version of AS and related firmware updates (hoops = I don't have time to do this thing for you).
Just FYI, a standard, 15 inch 4PP420 is on ebay for $1500 and a new one isn't terribly much more, so if this down time is hurting you more than that and the VNC server isn't running on the panel, just order a new one. You can swap the interface card and CF card yourself and be up and running in no time. If your panel's part number ends in -K## then it is custom and you're up **** creek because you'll need the same part number to replace it, even if the only thing different from standard is the logo on the front. If it includes the name of the OEM like MACHINEMAKER-02 as the part number, then you're extra screwed because you can't even order it from B&R because they've agreed to let the OEM force you to buy from them. Without the project software to change the part number of the target to a standard part number, you can't just swap CF cards to a different part.