At least
The Tech Guys got it right on the 2nd try... my PC is back with me and has a replacement battery! Huzzah. The battery was one of the key reasons I chose this particular laptop - it's got an 8-cell battery and the life is great, 3-4 hours is not unexpected, and that's with an external 2.5" HDD connected drawing power from it, watching TV/films.
I virtually have a new PC now, with new motherboard, RAM, HDD all provided on the first return for no apparent reason.