Boot the system up from a rescue image. Then investigate the system:
mdadm -Ebsc partitions
mdadm -E /dev/sda1
...
Try to figure out if it's just one disk that's gotten out of sync, if yes, then you're in luck. Recover the raid's with:
mdadm -Ac partitions -m 0 /dev/md0
mdadm -Ac partitions -m 1 /dev/md1
...
if needed add the -f option (i.e. for raid5 that has 2 out of 3 disks available)
now if you had logical volumes check those
lvm lvscan
Activate them to get them in the /dev/ tree
lvm vgchange -ay
And now fsck everything you can. If things look good and the faulted disk is just out of sync due to the power loss, then add it back
mdadm /dev/md0 -a /dev/sdc1
...
wait for the raid to sync itself
cat /proc/mdstat
Reboot...