The 2010 MacPro can have connect whatever display the graphics card will support. The usual graphics connection is either DVI (which you are currently using), or two mini DisplayPort connections. You COULD connect displays to all 3 connections at the same time, if you have a need for more than one display.
So, to answer your question, you can get your preset display repaired. If it is an older display, that might not be worth doing.
Or, purchase a display that you like. Look at the connections that are on the replacement display. If it has a DVI connector, then you can use the same cable that you already have. The new display may even come with the correct cable that you can use. Or, it might have an HDMI connector, and you would need an adapter to change HDMI to DVI, or HDMI to mini DisplayPort. You can find just about any combination of plugs to connect to most any display that you might like.
So, I suggest that you look for a display that you like, at a price that you can afford. As usual, price tends to vary by the size.
Decide what size you want, the features that you need, then do your homework by finding out what video connections that display will use.
Some have only one choice, others might have as many as 5 different ones.
You can also return here if you are undecided, with the brand and model number of one or two that you might be considering.
There are no hard and fast answers, as the correct display is determined by YOUR needs - and your budget. There is a huge number of choices. You will seldom find a display that CANNOT be used. All it takes (usually) is the proper adapter to connect to your MacPro, and that's all you should need.
I think a good site to look is
Amazon.com. You can search for various displays, sorting by size and price, also sorting by the video interface.