The BSI (battery status indicator) resistor holds to switch the device to local mode mode or test mode status, if this resistor is faulty or damaged it will result to local mode and test mode problem on nokia 6610 and 6610i.
Nokia 6610 and Nokia 6610i Local Mode and Test Mode Solution
Replacing the 47K BSI resistor shown on above solution may possibly fix the problem. The BSI capacitor which is mounted located near the battery connector also caused the device turns to local mode if damaged, replace these capacitor also. Some mobile technician just remove it, but not recommended from the experts. If the resistor is not present it will result to flashing problem during servicing happen again.