Thanks for the answers.
I have already tried a new PSU, with more power with exactly the same results. The first boot is always for the same amount of time.
I have been advised elsewhere to update the BIOS, as it may have been shipped with a generic BIOS and not one specific to that PC. Indeed the Read me on the Support disk that the PC came with seems to support this. Therefore I will follow the instructions offered and try to update the BIOS, using the makers update software.