Hey Ferret76,
I think nobody can say how much a repair for this notebook costs. This is depending on the spare parts and working time from technician. There are some many different spare parts available for each notebook and so nobody can answer this question at the moment. You should speak with a technician. They can check the notebook and give you an estimate for repair.
But before you go to an ASP you should clean the notebook. Maybe the dust is blocking the fan and so it’s overheating and switching itself off. I also clean my notebook. I do this every 4 months and follow these instructions:
http://aps2.toshiba-tro.de/kb0/HTD7A01ZZ000AR01.htm
Good luck!
