iMac 24" A1225 Optical drive stopped working for no reason

There are two reasons you can face here the first is the drives head is dirty. You'll need to get a CD/DVD head cleaning kit to clean the head. Sometimes a quick blow of compressed air though the slot can do it but if you haven't cleaned your system out of all of the dust buildup inside that could make things worse! I would follow this IFIXIT guide: iMac Intel 24" EMC 2134 and 2211 Optical Drive Replacement to get the drive out to then clean as well as clean out the rest of the system using a soft paint brush and a can of can'd air.

The other possible issue is the disk you are putting in is not able to be read/write by the drive in your system. The early iMac's 8X SuperDrive 4X double-layer burning (DVD+R DL/DVD & RW/CD-RW) only supported:

• Writes DVD+R DL discs at up to 4x speed,
• Writes DVD-R and DVD+R discs at up to 8x speed,
• Writes DVD-RW at up to 6x and DVD+RW discs at up to 8x speed,
• Reads DVDs at up to 8x speed, writes CD-R discs at up to 24x speed,
• Writes CD-RW discs at up to 16x speed, [and] reads CDs at up to 24x speed.