Install the drive(s) inside a (normal) computer with SATA ports and check if they're working OK there, to rule out the USB enclosure messing with communications.
In any case, I'd recommend exchanging the burner / returning them under warranty as they definitely shouldn't have problems recognising blank media.
You'll have to read some forum that deals with X360 games, as it's not something we can help you with.
Now if you have a problem with ImgBurn specifically then please post the log of the failed burn.
Update your burner's firmware and try burning at 16x.
If that doesn't work then try with better quality discs, such as Taiyo Yuden CD-Rs (best quality), or even Sony CD-Rs (slightly better-than-average quality).
ImgBurn doesn't convert anything, it burns as-is, so you probably need to convert your video file(s) with something like DVD Flick, DVDStyler, ConvertXtoDVD or similar programs.
Also try burning at 4x and 6x.
You could also try cleaning the drive with a lens cleaning disc, or even manually if you know how to do it. The real problem is that slim burners are rubbish, especially when it comes to burning dual-layer media.