You do need to find out why your battery isn't charging. It could be a bad battery. It could be that your charger has gone bad. If you disconnected the battery over the winter, did you reconnect it correctly? Black is not negative!!!
However, to answer your other question...Yes, you do need a properly charged battery to use the slides. The battery charger puts a relatively small amount of current into the battery over a long period of time. This allows the battery to provide huge amounts of current over short periods of time, such as when you are running the slides in/out. The battery charger can't provide the amount of current needed for this task.
Gary and Pat Harkins
Dodge 3500, 2011 CF305SKP