Like you said your PSU is a 20+4pin connector which means the 4 pins can be removed, but if they can stay attached and plug into the motherboard, by all means do that. Also make sure that all other power cables are plugged in. Depending on the age of your motherboard and style, you might be required to connect a DIFFERENT 4pin connector to power the CPU which might explain why your computer isnt booting.
If possible post your motherboard specs or serial # here or if its a prebuilt computer IE DELL, HP, etc. post the maker and model number and Ill give it a good look over.
Edit: If you want PM me or send me a message through Steam and Ill help you work this out.