There are 9 LEDs (3 V each) connected in series in the LED strip. I tested individual LED with 3 V applied across, and it works fine, but when 9 × 3 V is applied across the whole strip, the LEDs are barely lit; each one shows very dim light and the power supply shows only 1 mA or less being drawn (the power supply only shows 0.00).
Another strip that works fine draws 100 mA. There are no resistors or caps on the strip.
What could be causing such high resistance in the path when individual LEDs work fine? If it was an open connection, the LEDs should not be lit at all, but they do light up faintly.