Amp light not working and one dead right channel

Without knowing how it's actually laid out, I'd surmise the output amplifier transistors in the right channel are shorted, the fuse for that channel may be blown, and the speaker protection circuit is keeping it turned off. Most amplifier speaker protectors disable both channels if there is a problem, but yours could be different. I surmise the lights you mention are directly connected to the speaker protector chips and indicate readiness for normal operation. If it takes a few seconds for them to come on after power-up, that lends credence to my hypothesis.
Unplug the amplifier, open it up, and measure the resistance from the right channel output to each of the output power supplies (or to the fuse for the output power supply for that channel, if present). If one or both is very low (i. e, close to zero), you have a fried transistor. If that is the case, it is probably a good idea to replace the complementary transistor connecting the speaker to the other power supply even if it tests good; it may have been overloaded when the first one shorted. In many amplifiers, the transistors are inside a hybrid amplifier module, so you would have to replace the entire module. In some amps, you have multiple transistors in parallel; here you can probably keep the transistors that were in parallel with the failed unit, but I'd still recommend changing the complementary transistors.