need spec for resistor (soundstream amp)

Have you actually verified that a resistor in the input circuitry is "fried"? The quoted symptom of "doesn't turn on" is not specifically indicative of a fried resistor in the input circuitry although it might prevent the speaker from producing any response to an input signal. If indeed a resistor in this part of the circuit is fried, it would tend to indicate that some other component/s in the input circuitry are also defunct.

Does the "power on" indicator light?

when i put power to the amp, the red "power" indicator lights. When i send a turn-on signal, the fuse blows and the "fault" indicator lights.

I'm pretty sure the resistor is fried, because it is burnt black and there is marking from smoke on the adjacent components. whether that's the only thing fried, i don't know. But i can't identify the resistor because the bands aren't visible anymore.

My idea is to fix the part that looks like it caught fire, then go from there. I'm already bidding on an identical amp on ebay, if i win that i'll use that one and look at it for reference to fix this one as a backup.

This certainly indicates that parts OTHER than the fried resistor are involved. It is because OTHER part/s are also cooked which caused the resistor to fry in the first place and the fuse to blow.

Replacing ONLY the fried resistor is a surefire way to cause its demise next time you power up. You have to find out exactly which components are fried and replace them all at the same time.

I doubt very much that Soundstream will make schematics available so you either have to fault-find by labour intensive means OR give the amp to a car audio repairer who knows the Soundstream amps.