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It's hard to see exactly what has shattered from those photos, maybe some from a side angle would help along with a description?
It looks to me like just the indicator which tells you the selected gear has broken off, but I could be wrong. Will the shifter not shift gears at all?
I don't know too much about the inner workings of these modern STI levers, but it looks like it's taken quite a hit. Seems like something inside was bent or snapped causing the levers to jam up?
If you can't get it working, you don't necessarily have to be bikeless. You could adjust your low-stop on the rear derailleur to make the rear gears automatically default to a more bearable gear, and you should still have use of your front derailleur. Not ideal, but it'd perhaps get you out on some flatter rides until you can get it fixed/replaced.