the range on the old motorola keys is bad, the new NEC keys are far better. The old keys also kill their batteries quicker.
the starting function of the key does not require a battery, it is powered up inductively from the EIS itself, you can stick your key with battery removed and the car will start.
In your freind's case - he's on the losing side as his car is gray market import, whenever a car like this is bought expect such issues because the local dealers will flat out refuse.
Your freind has an EIS failure, what needs to be done is to replace the EIS with a new one or rebuilt one, there are some places who do it in EU and also in UK. the old keys will work when its done correctly. I have seen it done here. There are some testing tools to verify the inductive ring is sending power to the key - if that fails the EIS wont operate as the key never sends the IR signal to the EIS, while the keys will lock unlock doors etc.
ask your freind to try aiming a hair dryer on the EIS and retest - if this started happening on the onset of winter.