Took car in for oil/filter change and ".

Your battery is at the age when it can be expected to fail due to lead flaking off the plates. When that happens, the charging current going through the plates has less material to act upon so they get hotter than normal and cause the acid to bubble excessively. That bubbling causes the acid to reach the underside of the top of the case where it splashes and condenses, and some of it seeps out between the posts and case. THAT is the cause of the corrosion around the cable clamps. When you see that corrosion, you can guess the battery is going to fail within the next six months, as yours did.

It sounds like a smaller wire broke off one of the battery cables and the generator is not recharging the battery. Evidence of that is that it took four days before the engine wouldn't start. The place to start is by having the charging system tested, but I'd have that done at a battery store, not the dealer. They will test the battery too. $70.00 is a lot to pay for a simple battery terminal cleaning, and they should be ashamed to charge $170.00 for a new battery. I recently bought one for my '88 Grand Caravan for $65.00, and it took less than ten minutes to install it. Most battery shops don't charge extra for installing one of their batteries, and some do the charging system tests at no charge if you buy a new battery.