Electrical problem preventing starting

Battery fine. Key inserted in ignition, ignition and panel lights display as normal. Key is turned to start; no sound, panel lights dim. As key is released engine starts and runs. As the engine warms the fans cut in and out intermittently with fluctuating current to them. Observable as abnormal increases/decreases in fan speed consistent with intermittent electrical contact.

If engine is switched off and attempts to start it again are made, there is no sound at all; panel lights dim. When key is removed the starter can still be heard turning very slowly. Battery must be disconnected to prevent this continuing. There is significant heat at the positive terminal of the battery whilst the starting process is ongoing such as to cause smoking at the terminal.