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Thanks ChuckFickens. I did as you suggested, taking the two memory modules out first. I cleaned the connector pads and vacuumed out the sockets. I reinserted the modules and tried the PC again. No joy - same problem as before.
I then removed the graphics card, cleaned the connector pads and reinserted it. This time the PC failed to boot again, but the error beeps were missing. This led me to think that it might be the graphics card after all.
The graphics card has two output sockets and obviously only one of them was being used. Due to the fact I was connected up to a CRT monitor, the blue monitor cable screws into a white adaptor and the white adaptor screws into the graphics card socket. I removed all the connectors, made sure the card was located properly and plugged the monitor into the other unused socket instead. The PC booted up like a dream.
I can only put it down to a dodgy socket as there might well have been an excess of mechanical stress on the socket due to the thick monitor cable, the socket and the adaptor being plugged in.
Thank you for pointing me in the right direction - it's much appreciated!