We're just experiencing the same issue with my wife's 2008 V70. Battery was new last summer, but terminal corrosion has been an issue for some reason. We'll clean that up first. We'll also try replacing the fob battery.

She tells me that she got the car to start after a few tries, but had no IP (instrument panel) and no signals. Headlights worked though. On a subsequent re-start, everything worked normally, except that the check engine light is on, for the first time in the five years we've owned the car.

I'd appreciate knowing what you found out at the dealer.

Aside from a leaking washer fluid reservoir, a bad brake caliper seal, and a split CV joint boot, this has been a superbly trouble-free car over 65,000 miles (total of about 120,000 on it now).