Lets try the obvious, cheap & easy first.
1. Copy the disc that still works on to the computer and keep it there as a folder. Burn a second backup disk using that folder as the source. We don't want to loose any more. I would also put the files onto a pen drive (usb stick) and keep it safe until this is all resolved.
2. If you look at the faulty disk edge on to the light can you see any scratches, coffee, bits of pork pie, phlegm, sneeze fluid etc etc? By the way a disk burns from the middle outward - not that it will change anything here except that if there are scratches they obviously matter if they are in the data bit - see 3.
3. If you look at the disc held edge on to the light you can see the colour difference between the bit that has data on it & the bit that hasn't. Are the still working and the non working disk the same? If they are the same then you still at least you still have most of what you had.
4. Did you finalize the disk so that it will play on other computers?
5. Try the malfunctioning disk in a second computer & keep your fingers crossed. If it works burn at least 2 new disks. The easy way to do this is to copy the disk into a folder on the hard drive of the 2nd computer & then burn a couple of disks from there. I would also put the files onto a pen drive (usb stick) and keep it safe until this is all resolved.
If you still haven't got a solution it gets trickier.
Good luck.
I know that this isn't the time to mention it but home burnt disks should never be relied on to secure data. I use 2 independent hard drives. There is an old saying that goes something like "if you don't have data in at least 2 independent places from the one that you are currently using consider it lost."