A couple of things. A full range speaker has a crossover in it, It has a few components, notabley coils and non-polorized caps.
First, you need to swap speakers - this tells you that the speaker is the problem. Each speaker has a voice coil. checking the resistance of each voice coil with the crossover disconnected is at least a start. Making sure that the leads leading to the speaker have continuity is another. If the impedance is 8 ohms, the resistance will be somewhat lower,, say 6 ohms or so.
Large speakers can be tested with a 1.5 V battery. When a battery is attached to the voice coil with the proper polarity, the cone pushes out.
There can be internal fuses in a speaker enclosure too. Mine are behind the grill cloth and the speakers are removed after the cloth is removed.
Scratchyness is usually the result of a voice coil getting hot. The cone will have friction when depressed manually.
You can test each speaker individually at low power. The tweeters would be susceptable to damage at high power levels.
The surrounds could be damaged.
Check the crossover for bad connections. Capacitors in the crossover can be the cause of bad sound as well. These MUST be replaced with non-polarized caps of the proper voltage rating or higher.