Power Toothbrush

I HAVE A FAN THAT BLOW OUT OF MY APARTMENT. THUS, THE SCREEN GETS ALL DIRTY AND CLOGGED. I HAVE TRIED, RUBBING ACHOHOL, SOAP AND WATER, WINDEX, (I USED A TOOTHBRUSH)….I HAVE NO ACCESS TO HIGH POWERED WATER OR STEAM SPRAY….CAN YOU HELP? THANKS…GLEN