Flickering Dash Lights / Wont Start

Last night at a friends house our van wouldn't start. The dash lights flickered, no clicking from starter, so I thought dead battery. Gave it a jump (it started right away) and it ran just fine till I got home through the stop and go of city traffic. Approx 5 miles. Once home I shut it off and immediately tried to start it again - nothing but the flickering lights and no clicks from the starter.

There was some corrosion on the terminals that we brushed off prior to jumping it last night. This sound like a dead battery? Dirty terminals? If it wouldn't stay running the entire way home I'd think alternator...

Appreciate any input you have.