Once you are sure the derailleur and wheel is in the right place, the chain does not need to be longer than to work with the largest chainring and largest rear sprocket combination. Have a look at the Sheldon Brown and Park Tool websites, and feel free to post pics of your bike here (pref taken from the side).
As mentioned already by Cunobelin, and worth repeating in case it got lost in the noise, the freewheel or freehub could be to blame if the chain is going slack when coasting. Unfortunately it's a classic symptom of a knackered freehub.