Make sure you replaced the protection diode with the same orientation as the original ie: look at the silkscreening on the board to see that the line is correct with the diode. The band on the diode should be on the + side of the board.
When the on switch is on, there are a number of parts that get 12v from the power rail. The final, audio amp, voltage regulator, and a few others. You will need to look at the schematic to see them. If any of them are shorted; that can cause the fuse to blow. You might have to unsolder each power lead to each of these parts to isolate the problem part.
http://www.cbtricks.com/radios/cobra/29ltd_29ltd_st_29wx_st/graphics/cobra_29ltd_sm_sch.pdf
Whatever you do, do NOT put a straight conductor in the fuse port. Smoked parts will follow! Make certain that you have the right fuse in the fuse holder. Too small value of a fuse will pop, and one that has too large of a value (ie: 5 amp @ 12v) can cause a fire or a board meltdown. Make sure! Burned traces are nasty to fix.
However, my first blush guess is to test the voltage regulator, and especially the zener diode (D22) in that circuit. It is a bit difficult to test a zener; so it would be easier just to replace it outright (8.5v 1/2w). Been there; done that. The first time I found a bad zener, I just touched it with a screwdriver and it fell to pieces. Not always. Funny that the schematic doesn't show it as a zener, but it is:
http://www.digchip.com/datasheets/parts/datasheet/192/HZ9B1-E.php
Also check the output voltage of the regulator once you replace the zener. If it is 8/9v out of the regulator then the zener/regulator are ok. But to do that, you will have to unsolder all of the parts that get 12v to the board w/o snapping the fuse. Or, just lift one end of the zener. See if it is cracked or damaged. If so; you've nailed it. If not; I'd replace it just the same . . .
There are other members here that can also give you some tips to check - that have a LOT more experience and knowledge than I do.