Karozza, it could be the key, or it could be the Keyless go receiver/antennas. Needs Star Diagnosis to really find the issue.
As to distance, the cars are both Infra Red, and radio based. Radio used for distance, IR when close (and you get functions like being able to hold the key and wind windows (and roof) up and down when using the IR system).
Thus it sounds like the radio based bit is broken. This can be a key fault (try the other key!!) or a blown fuse, or an antenna amplifier fault. If it is an antenna amplifier fault, you are some what in trouble, because the antenna amp is behind the dashboard (at bottom corners of the windscreen) as the antenna are in the front windscreen on a SL, and you have to remove the dashboard to replace the amplifier. So, (a) try the other key (b) check the fuse diagram and all the fuses listed for central locking (pretty sure its one in the rear fusebox behind right front seat in that stowage compartment) first.
I'm pretty sure the Keyless Go system and it's antennas are very separate to the remote fob antenna, and thus unlikely to be the same fault, but its a while since I pondered the SL wiring diagrams for this stuff.
Cheers
Richard