Does it say PCG-FRV31 on the top near the keyboard? Somebody else online had PCG-9L1L on the bottom but it's more commonly referred to as PCG-FRV31.
If so, here are
manuals for it, including specific instructions on swapping the CD/DVD drive. Looks pretty easy compared to many laptops, just a few screws.
Here is a replacement specifically for the model but I wonder if it is used in other models as well. Ah yes if you search for the drive model number 'SBW-242U' you get
tons of results. Looks like you can get one for $25-30 with shipping, not too bad.
Just watch for ones with weird-shaped vendor-specific faceplates, although it looks like you could swap the faceplate from the broken one. Some even come without a faceplate so it should be possible to swap them.