There is also a possability that BOTH the alternator and battery are shot. If you charged the battery all night and your charger only said 70% charged your battery may have leaked and now is too low to take the charge and you probably need a new one because with new batteries you cannot just fill them back up with distilled water and try to charge again because they are sealed cells.

 

Sounds like you have a marginal alternator in the past, continued battery problems, and now a used alternator that won't charge at all (based on warning light). While you are at the auto parts store invest in a digital volt meter, they are handy for lots of things. Mike's right, a "12 volt" battery does not charge at 12 volts. Since you replaced the alternator, might want to re-check your connections. Hope the store is not too far away, because you will repeat the original experiment - battery exhausted, vehicle operation ceases. By the way, auto batteries are designed to fail, so they can get cyclical repeat business. Some of the same battery companies make units for the telecommunications industry that are rated for 20 year service life.