Thanks k7elp60, any suggestions you could provide would be great. The PC at the moment is wired directly to the 12V battery, would be best to steer clear from inverters and such. The PC is specifically made for automotive applications, hence it operates off of 12V and draws 7 amps on full operation. On sleep mode it draws around 100-200mA, so I suspect I may get a week or two running in sleep mode off the auxiliary battery (assuming around 50Ah, but doesn't need to be this high). I have a DC to DC converter that is between the 12V battery and PC, so any fluctuations in voltages (on starting car and such) will be smoothed on the output of the converter.
Blars, great to hear that the batteries need not be matched. Would simple mechanical relays do the job?