Sorry Stuart, I can't say with certainty because I don't have an IS200. On the RX the windows may fail to operate properly so the procedure is to go round each door and press the down switch until the window is fully down then hold for 10 seconds, then do the same for window up, after which they should all work correctly from the main switch panel in the drivers door.
I've never heard of any car, young or old, Lexus or Vauxhall or whatever, having trouble with the immobiliser. Radios yes, windows yes, sunroof yes, but never immobiliser so if it was me I'd just change the battery. If you're still worried, I know you said that you haven't got a second battery but have you got a battery charger? Or a second car with jump leads?