Your CD-RW media is the original type. CD-RW media comes in three generations - the original type, which stops at 4x, High Speed, which goes up to 10x (and no higher, so far as I remember), and Ultra Speed, which is certainly capable of 32x operation, though some Ultra Speed discs have a lower maximum speed. The three generations each have a different formulation of the recording layer.
No drive is capable of writing a higher media generation properly, as it doesn't know how to write that media correctly - I've got a Plextor SCSI CD-RW which is a High Speed drive (capable of 10x operation on CD-RW). That drive won't write Ultra Speed media properly - if, indeed, it tries to write it at all! I don't have any US CD-RW media to try - I make very little use of CD-RW media.
More controversial is the issue of whether drives of a higher generation are capable of writing lower generation media correctly. To an extent this is probably drive dependent - it depends how well a drive is set up to work with the original 4x maximum CD-RW media. I have heard of particular allegations of incompatibility between High Speed drives and the original 4x CD-RW media. This issue is supposedly worst if you're trying to write that media both in a more modern drive and a 4x maximum drive.
High Speed CD-RW media seems to cause little to no problems in Ultra Speed drives. Ricoh 10x High Speed CD-RW media seems to work fine in my NEC ND-2500A (which is an Ultra Speed drive, but only capable of a relatively lowly 16x maximum speed on CD-RW - this drive is far more optimised as a DVD writer).
Your new drive is Ultra Speed capable - 24x on CD-RW. Your 4x media is probably rather old (as well as slowing your drive to a fraction of the speed it is capable of). If it's Memorex, it might well be CMC Magnetics media, which is a brand that some regard as of somewhat iffy quality - I was once given a 4x Memorex CD-RW which was CMC Magnetics, and decided not to use it other than as as an example of original CD-RW media for test purposes.
Putting all this together - I'd be inclined to try some new Ultra Speed CD-RW media of a quality brand - or possibly High Speed CD-RW media of a quality brand (Ultra Speed can still be rather expensive). If it works, then not only have you got some reliable media, but your drive will work much faster as well!