You need to establish which of the two possible causes are making it refuse to read. The only way to go about that is to discount one cause.
In the case of a DVD - you need to burn the disc (you can use a re-writable) in DVD-Video format.
I don't know what format your existing method has resulted in.
Place the errant disc into your computer, and using Windows Explorer (or whatever it may be called on your version) look at the folders on it and the contents therein. A DVD-Video disc contains one or two folders:
Audio_TS (if present it should be empty; may not be present at all) and
Video_TS which should contain various files with extensions .bup, ifo, and .vob. with the vob's being the larger files.
If your disc is not exactly like this, it's not a DVD-Video and that may explain why the player is refusing it - not the disc, but the data structure causing the refusal.
For CD - the baseline format you'd expect the player to recognise is CD-Audio. If your disc isn't properly CD-Audio format, again, that might explain the refusal. In Explorer, a CD-A disc appears to contain one file with the extension .cda representing each audio track, and the files are small - usually show as 1kb size (in fact it's a sort of shortcut, not the audio data).