I've been playing around with the patcher and have successfully gotten several games to boot off the NeoFlash 512Mb that I got in the bundle from IC2005.com.
I'll assume that the NEO Power Kit and Slim Loader 3 are properly installed. A good test for this is putting the Power Kit into GBA mode and burning one GBA rom to the card and booting the GBA card from the DS's menu. As long as the GBA game works, then you know the Power Kit is working.
Make sure the Power Kit is in DS mode by running the "NDS Mode.bat" file that is placed on the desktop when the Power Kit is installed.
Download the MK4 v1.0 patcher, extract the zip file, and drag a DS rom onto the "MK4-Mini Patcher V1.0.exe".
For example, I dragged "Castlevania - Dawn of Sorrow(U).nds" onto the .exe file and a patched "Castlevania - Dawn of Sorrow(U).nds.gba" was created.
I plugged my NeoFlash 512 into the Slim Loader, and plugged it into my USB port, and ran the NEO Power Kit. I added the .nds.gba file and then burned the rom.
Once it finished, I put the NeoFlash 512 into my DS Lite and turned it on. I booted it from the MK4-Mini and got a black menu. I then pressed B to make it boot from the GBA slot. The rom started and everything worked fine. I did not try to go into the MK4-Mini's menu because I get the same problem with it asking to format the NeoFlash card, etc.
Just tell the MK4-Mini to boot from the GBA slot and it will work fine.
I'll try to clean up this post and add some screenshots when I get home from work. Until then, good luck.
Games tested and working with this method:
Castlevania: Dawn of Sorrow (U)
Advance Wars - Dual Strike (U)
Lunar - Dragon Song (U)
Mario Kart DS (U)
Trauma Center: Under the Knife (U)
Tested, but not working:
Mario and Luigi: Partners in TIme (U)
Seiken Densetsu DS - Children of Mana (J)