The amount of wrong information in this thread is absolutely baffling... Let me try and sort this out for you guys...
The DS does have the processing power necessary to "emulate" the GBA in a way (since the hardware is pretty much identical, it's more a matter of mapping matching commands) the problem has never been about the processor, the problem has been with the media (IE, where the rom is stored) and RAM.
A quick explaination of what RAM does... RAM is used to store variables, or things that change as you play. RAM also has another use though, and it's this second use that truly divides GBA from DS... and that is, it can be used to store data for quick access, if the media is expected to take to long to load it.
Now when the GBA was first released... RAM was still relatively pricey for extremely portable electronics so nintendo went with 256k which is miniscule... Programmers really can't do much with that tiny amount of ram, so nintendo, to compensate, had GBA carts manufactured. These carts (like NES/SNES carts before them) had (relatively) fast access times to data, especially random (non-sequential) data. So while the ram on the GBA was incredibly limited, much of the GBA data could quickly and easily be run straight form the cartridge, leaving more of it for the variables necessary for games. The problem with these game cartridges though is that they can be fairly pricey (between 10-20 depending on size with little hope of prices dropping over time) and that meant both nintendo and developers made less money for each game sold.
In comes the DS. Several years later now, RAM prices have dropped considerably and the DS stepped up to 4MB of ram (16x as much as a GBA). This frees up a lot more room for game data to be stored in the RAM so nintendo could thereby skimp on the cartridges. Enter the DS Slot-1 card. These game cards, while able to store more data, also used much slower memory (this is why some DS games have loading screens on occasion, while zero GBA games to my knowledge did) and were much cheaper to make (around 5-10 USD per cart, though that price probably has since dropped as well) so both Nintendo and developers made more money for each game sold making them all much more profitable.
So with that knowledge laid out, let's go back to the original problem of why the DS can't play GBA games from SLOT-1. GBA games are programmed with the belief that if they call data from where the game is stored, it will be executed pretty much instantly. SLOT-1 Devices do not have this ability, they do not have the access speed (especially non-sequentially) that the games require and will thus instantly crash the game.
"But SNES games can be emulated and they are based on cartridges!" Good point! Why do SNES games work but not GBA then? The difference is that SNES games are small, the vast majority under 4MB in size... Exactly the size of the DS's ram. The games work because the entire game is stored in the super fast ram and thus can pull that data as quickly as the game needs. Your typical GBA game, however, is 8-16MB with the largest at 32MB and therefore has no chance of fitting in 4MB.
"But there are SNES games larger than 4MB!" Also true, the author of the emulator uses a couple nifty tricks to handle this... The first and preferred method is if there is a SLOT-2 device with ram, it will use that. The RAM in SLOT-2 is fast enough to handle them. The second, much less preferred way is to freeze the game when it calls for data out of ram. The emulator then clears out a portion of ram and puts that data into play. This has the effect of greatly slowing the game down in certain situations. Now imagine this problem several dozen times worse as GBA games are much larger and would be pulling data not in RAM far more often... yeah... not pretty.
So where does that leave us in general? Well the DSi does have 16MB of RAM, which would mean that there shouldn't be a problem (in theory) of playing the smaller GBA games without any slow down when DSi mode is cracked... but the larger games would still have a problem no doubt.
As for GBA slot-1 on a regular DS... you're not going to get it. No emulator author is going to spend their time on such a project because they know what I've told you all right now, that the RAM constraints (or the data from slot-1 restraints, whichever way you want to look at this problem) are such that there is no software workaround and even if there was one, it would be pointless since you can easily buy a cheap peice of hardware that would make weeks/months worth of work obsolete and run better.
-inhales- Okay... I think that should cover every misconception in this thread... my only fear is that I made it too big and no one will pay attention. If anyone is interested in discussing anything else on this topic, or if anyone would like me to go more in-depth or reexplain something let me know.
(edit) Just a quick amendum, DanthemanMS did have this understanding, I kind of skimmed over a couple of posts when it didn't seem like anyone got it, I still didn't want to delete all of this though as it did take a good portion of my time and it's a bit more explainative and hopefully in simple enough language to follow.
