From looking at the drawings, there are two power supply fuses in this (your?) Kaboom, on, it appears, the power supply board. This is pretty standard for Boomboxes.
From looking at your photos, it looks like the power supply board is underneath the board on top. The power supply board will, naturally, be right behind where the AC input comes into the Boombox...usually. It's kind of easy to find because it's the one the power cord plugs into.
If you look at page 18 of the PDF, I believe, you will see that several connections on the power supply board are circles labeled "1" and "2".
These are the power and ground connections for the batteries (connectors CN602 & CN603), the transformer (connectors CN604 & CN605), and the main AC power input (connector CN606). At least, that's what's on the drawing.
Are you following me?
Do you see the two fuses? They are labeled F601 & F602. They are, on the drawing, inside a gray shaded box. You can't miss them. They also have a triangle with an exclamation point inside it next to them. All that means, as the note on the drawing says, is that they are critical for the prevention of fire or shock. These are the two fuses you should check. They are 4 amp, 125 volt fuses. The F601 & F602 numbers should be written on the circuit board. If not, you'll have to become a tech and follow the circuit paths, first from the positive side of Battery connector CN602 to fuse F602...and then back from pin 4 of the Board connector CN101 to fuse F601. Once you find them, check them. Put a meter to them and check continuity, or just put them up to the light and see if the filament inside is in one piece. If they are still good, they are not your problem. You'll need to work upstream, following the drawing, until you find the fault that has turned your masterpiece into a boat anchor.
You can do it. Just follow the drawing. Looks to be pretty standard for these power supplies, although I can't say for sure, as I haven't been inside my Kaboom in at least 5 years. At the very least, the fuses will almost always be close by where power enters the Boombox and are usually contained on the circuit board where the transformer is.
Let us know how it turns out.