Please help. Cannot turn the soundcraft gigrac 600 on.

Have you tried contacting SoundCraft directly ?
Here is a link for a part request.
Hope it helps,
It would also help if I knew where you are in the world, I am in Canada, here Soundcraft is distributed by SCMedia in Toronto
https://www.soundcraft.com/en/support/parts

Your unit is telling you that there is something wrong. This can be in two places, your power supply is shutting down (thermal) because of a component fault, and or your Amp(s) are overheating due to also a component fault. My guess, for what it's worth, is one of the amps has a bad final so I would disconnect the power supply from the amps and see if the unit keeps running. If it does than re-connect one amp at the time and see what happens. This should get you a fair way in to finding the fault. Have fun.

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There is a bad amp in that divice that is causing an overload. The device then shuts down. This is not something that you can fix yourself. IT requires special diagnostic tools and troubleshooting as well as soldering ability.

http://www.soundcraft.com/contacts/contacts.aspx

You should be using Dynamic mics such as a Shure SM58. They go into the first FOUR channels and if there is excessive gain and distortion, push in thee Pad button below the connector for those four channels. Inexpensive consumer microphones used with some Karaoke home systems are not suitable for this unit. You should be using XLR cables on the mics (balanced lines). The Pad buttons reduce the gain by a fixed amount of -20 Db for mics that have too much output to be controlled by the gain controls right above the connector. Ideally those should be no less than 12 o'cloock for good signala to noise ratio. Additional channels beyond the first four do not have as much gain and they do not have the -20 Db pad option.

The resistor is acting as a fuse and will continue to blow until you fix the REAL problem. LIKELY the filter capacitor(s) beyond the bridge rectifier are failing. One needs to use test equipment to measure the current through the resistor and see if it is reasonable. The capacitors can heal briefly and then start to short. One should also check the rectifier in operation with an oscilloscope as one diode could intermittently short.

Checkout Tools2Parts:
http://www.tools2parts.com/Bussman-ABC-10BC-p/1031-1710.htm