Slim Specific Issues
The one thing we do know in regard to BC on the Slim systems is that it won't work on the $GB model without a proper hard drive installed. The 4GB Slim doesn't actually have a HDD installed, just 4GB of onboard memory, so BC won't work on it unless you install a HDD. The 250GB (or bigger) Slim systems should play BC games just fine.
Older Model Xbox 360 Issues
A question that comes up every once in a while that seems to stump everybody is some variation of "I just got an Xbox 360 but it won't play original Xbox games. Why not?". It is a tricky question because there is no reason why you shouldn't be able to play OG Xbox games on your Xbox 360 (as long as they are on the BC list) and you have a hard drive attached to your 360. The system variations (Arcade, Pro, Elite, etc.) don't matter one bit in regards to backward compatibility as long as you have a hard drive attached to the system.
Then it hit me - If it isn't the system that is preventing backward compatibility from working, it must be the hard drive. With a little research it seems that a common thread between people that can't get backward compatibility to work on their Xbox 360 is that they bought their hard drives off of eBay.
Why Is This?
Simple. Certain eBay sellers try to make more money by buying 20GB official Microsoft Xbox 360 hard drives for cheap, and then putting larger laptop hard drives into the official 360 hard drive case and then selling them for less than an official drive of the same size would be. Now, technically, these hacked hard drives are the exact same thing as an official one, at least as far as parts go. They will function exactly the same as an official drive. But many of the sellers that sell these drives forget (or might be just plain ignorant about) one important thing – to play backward compatible Xbox games, the hard drives need a special partition for the Xbox 360 to store BC-related data in. If the hard drive doesn’t have that partition, you can’t play backward compatible games with it.
What Can You Do?
There isn’t really much you can do other than just be wary. It can be hard to tell if a hard drive you buy off of eBay has been tampered with because they’ll look exactly the same as an official one on the outside. They might look new, but you can’t ever be 100% sure about anything you buy on eBay. Some sellers might have even made sure to partition the hard drive correctly so it’ll work and you’ll have no problems, but not all of them do and that is where the problem comes in.
If you don’t care about backward compatibility, you don’t need to worry about this. Everything else will function exactly like an official one. If you do want to use your Xbox 360 to play original Xbox games, you just need to ask the right questions of the seller before you buy a 360 HDD. Ask them if it is an official or hacked drive. And if it is a modified drive, ask them if it has the necessary partitions. If they don’t give you a straight answer or don’t understand the question, don’t buy from them.
So, to answer the question “Why won’t original Xbox games work on my Xbox 360” there really is only one answer – Your cheap eBay hard drive might not be as official as you thought and is missing key files that allow for backward compatibility. The solution - Buy official Xbox 360 accessories from established retailers, or if you want to save a few bucks on eBay, make sure you ask the right questions so you know what you're getting.