Ignoring remote issues for the moment, if the key won't start the engine then the transponder in the key is dead and you must buy a new key. The transponders in the keys just die after awhile (I've seen people complain after as little as 5 years) and it isn't a component that can be replaced with off-the-shelf components (like the rechargeable battery). The ignition and the key have to be paired so you will need to contact a BMW dealership to replace the key as BMW will have to manufacture it. This happened to me after I purchased my 2005 last year. I only had one key and it stopped starting the engine when placed in the ignition.
The dealership will need proof of ownership (vehicle registration receipt), proper identification (drivers license), and the VIN number of the X5. You will need to present these items in person and it can take several days for the key to be sent to the dealer (mine provided an overnight shipping option for an extra fee). Once you go in to pick up the new key they can program the remote (or you can do it yourself using the instructions you found).
[Dead] 2001 X5 4.4i w/ 139K miles (probable cracked engine block)
2005 X5 4.4i w/ 97K miles