I'm using a Kensington N3 adapter on a dell mini at home, it's on one of their older 120 watt universal adapters. I'm fairly certain one of the others in the kit fits the Inspiron's, I think I used it with an Inspirion 15something once. It's not the best solution, the plug is a bit loose and needs to be held in the mini with a tiny bit of folded paper, but it does charge it.
There are a couple other tips that fit, but don't supply the right voltage and won't power it.