A read-only filesystem (that shouldn't be read-only) usually indicates one of two things: the filesystem is damaged, or you have a hardware fault with the underlying disk or disk controller.
If the filesystem is damaged then you can fix this with fsck.
Faults with the disk are more common than the disk controller, since disks have moving parts and therefore a more limited life.
One thing that might help you: if you can get to a shell after booting, then run
— this will tell you what the last errors reported by the kernel were.