There is nothing to load on your cart for the m3 to work. The firmware itself is flashed onto a chip on the pcb. You would only need to place the firmware on the sd card if you were trying to update to a newer version.
It is starting to sound like your cart is malfunctioning. If you are not getting past the GBA splash screen then your gba micro isn't reading anything off of the m3 cartridge. This situation is no different than turning your gba on without a game cart.
This behavior suggests contact failure. You would have to dissamble the M3 cart, lift the pcb off the cart, insert a peice of paper/cardboard, reinsert the pcb and put the M3 cart back together. This method pushes the PCB out a little bit so that the contacts are also extruded. This would ensure that the contacts on the cart are making 'contact' with the gba slot reader. It would also help to clean the cart's contacts with isopropyl alcohol using a cotton swab.
If this does not solve anything, trying using various widths of paper placed behind the pcb. It may also be the case as per howdoidothat's instruction that you must solder the battery back onto it's original contacts. Also the extreme unlikelyhood exists that the program memory on the pcb has somehow become corrupted.."would only happen if you used the incorrect fw update for your card".