If the lamp holder has (as you say) "current" on both sides it suggests a wiring fault - mains voltage on each side of the lamp holder means that no current will flow through the lamp! To operate properly you need mains live on one side and mains neutral on the other - then current will flow through the load (the lamp).
Given your use of the word current when you really mean voltage it suggests that you don't understand electricity so take care - take advice - get an expert.
No it does not mean too little power to the fitting - Power is Volts multiplied by Current (Amps). If your lamp is not lighting then no current is flowing and no power is being consumed.
My guess is that the ceiling rose has been mis-wired. The fault as you describe it is very unlikely to "just happen". Get an electrician - good luck...
Richard Buxton, September 2008
