If you're not getting any interior lights with a new battery...as well as when you hooked up jumper cables...and you have the unconnected thick red wire...then as assumed...the positive battery cable appears not to be running to the high amp fuse box and the other fuse boxes. If this is so...looks like you may have spent a lot of money for an unneeded battery.
See the diagram below:
E53 Positive Battery Cable Run to starter/alternator/battery/fuses/engine bay jump start locations)
(You can see in the illustration below how the 2nd wire attaches to the BST (battery safety terminal) which runs to the high amp fuses and the other fuses in the right rear cargo area and up to the glovebox. Also how there's an explosive charge on the positive battery terminal which is a good reason NOT to hook battery cables directly to the battery if the engine bay location can be accessed.
)
