[frsimen]

That's rather unfortunate.

Have a good look to see if there is anything obvious that has burnt. Favourites would be low value resistors. Transistors and diodes can smoke but not show much change to their appearance afterwards. They will probably have been damaged, however. If you know roughly the area of the board that was in contact with the solder coil that would be a good place to start.

Next you should determine what, if anything, works.

Does the horizontal shift work?
Does the timebase run any time setting? Try with different trigger modes and sources.
Does X-Y mode work?

Check the power supply voltages after that.

Above all, make sure that your work area is tidy and free of anything that could cause a short to avoid even more damage!

Report back what you find, others may be able to offer more help once you give a bit more information.