Assuming you've done the obvious like update your drivers and checked Device Manager for faults:
This sounds like a signal problem, possible voltage regulation, in your audio card or hardware board. CD/DVD combo drives have something like three lasers: one tracks; one reads; one burns. They all get their basic instructions from the drive hardware ROM but the path signals themselves for each laser come from the audio driver and then is expressed electrically to the drive's ROM hardware. If the signal to the drive's ROM hardware is wrong or the current is too "hot" the drive simply recognizes the fault and stops working; it takes a couple seconds for it recognize. I don't know how this program is diagnosed, exactly, but I can tell you that I've heard from Expert Forums that it happens with certain hardware combinations.
If you have audio hardware matched to the drive manufacturer I bet your drive would immediately be restored to full functionality. Problem is, very few manufacturers manufacture both! Memorex, however, is an old name in the computer game; I doubt it's your drive that's the hardware problem. It's the path signal to the drive, and that means your audio board.
OR, you've got a rootkit. They're easy to get your computer inflicted with. Here's how rootkit copy-protection software works; you buy a CD from a music artist whose music is distributed by a bunch of shady a**holes like Sony. Because they're shady, they distribute the music CD with a hidden software installer on it that write to your computer copy protection software that prevents you from copying their products. That software is a handsome frog to detect, and a handsome frog to take out; sometimes they even rewrite your friggin' Kernel!
It's also a huge security breach of your computer. The problem with invasive rootkits of the sort I'm describing is that they invariably involve opening up a hole in your OS security big enough for Terabytes of malware to just march on in without you knowing a thing, particularly if it's Kernel-rooted. Sony got in trouble for just this sort of thing, and the "patch" they issued to correct their f*cked-up actions actually was worse than the rootkit it was supposed to remove; the patch only managed to weaken OS security more. Sony had to release a patch for the patch; how messed up is that?!
A lady in Maryland is suing, uh, Electronic Arts for just this infarction of her consumer rights (as I see it, it is a right to applied merchantability, that you are buying only what you thought you were buying. It's also injurious to you because you obviously don't want your computer made easily exploitable by virus attack simply because you like Lady Gaga or Kenny Chesney or whomever you like on a major label). EA games come with copy-protection software that you can't uninstall even when you uninstall the game. It just stays there and eats up resources. This is why I will never buy an EA game, or games from some other manufacturers.
I suggest getting a rootkit detector and running it (I use one called, uh, Blacklight, something like that) and see if there's one operating. If one's not, then you indeed have a hardware problem that involves either some soldering iron shenanigans or buying a new hardware card. I also suggest, personally to you, that you not play newer audio CDs from any major music distributor like Sony or Bertelsmann or Warner on your computer CD drive; use a CD conventional player and your mic-in jack and audio software like, uh, that free one, uh, what's it's name... Audacity! Yeah, that's the one. Audacity's good software: does a lot of things well enough for home use.
Me, personally, I listen to drum and bass (small labels) and world music (old and trusted labels) and techno (small labels) and really old classical music CDs (definitely rootkit-free) for the most part so I have little to worry about. All you fans of current pop music, though, I feel for y'all. Y'all probably got all kinds of mischievous software running around you have no idea about.
[size=+1]Have you tried burning other, different CDs, like a CD you bought, say, in the early Nineties? Who distributes the CD you tried to burn?[/size]