The TNC151 has plug in boards, including a power supply board. They are accessed by removing the top of the control. 5 small silver philips head screw is I remember correctly. The control switches the 24 VDC internally, it is not used for actually running the control logic. The control also powers the CRT. Unplug the CRT first as it is more prone to problems than the control and may be the reason the fuse is blowing. It could be the control or it could be a bad power supply board. A check out at Heidenhain may be in order. I hope you have a backup of your parameters.
George
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)