The plastic frame is in 4 pieces from the factory, 2 end pieces and 2 parallel side pieces, so from what you describe they are probably not broken.
The end pieces are glued close to the glass' ends then the other two are centered between them. I use speaker cement, it will stick to almost anything, including glass. Make sure not to have any glue squeeze out when you press the parts firmly together, if the glue comes even close to the touchpads you will experience faults.
Cleaning using handwarm water will remove most of the old gooey foam remains.
If I remember correctly none of the plastic pieces are alike, at least it's like that on some models, so do a test fitting before glueing. If the holding tabs are broken you will have to find another set of plastic frames.
Martin