Hi all,
if I remove the dirty filter media and squeezed it over my new filter would that work?
It will to some degree, but what ever anybody tells you, you can't really cycle a tank properly quickly. As Scatz says filter media would be better.
I know you need an answer now, so I'd try and keep up the water changes (at least 10% a day) and use a water conditioner that is active against ammonia.
For future reference, I keep a spare "biological" sponge filter in all the tanks, you can use an air powered sponge, (like these
http://www.ta-aquaculture.co.uk/Filtration-Air.htm say the Bio Sponge Filter FS 1604) or power the sponge from a power-head (I use a maxi-jet 400's), (you can pick these up really cheap on ebay), either of these options use hardly any power and are a back up if the main filter fails.
I don't even try and cycle my tanks now, I add a power-head sponge filter from an established tank, I plant them up (plants are great for water quality and I only have planted tanks), introduce some Daphnia, MTS etc and then just leave the tank until all the algae and water quality issues are over (usually 6 weeks to 2 months), then I introduce the fish.
The article here has links to a lot of information about water quality and filtration.
http://plecoplanet.com/?page_id=829. Best of luck.
cheers Darrel