EggXpert

I am building a computer and I have no video. on my Asus motherboard there are LED's that come on if there is an error, and there is one next to the CPU.

I have an Intel i5 750 Quad Core CPU. When I turn on my computer there is no video and after a minute it shuts down and it kinda smells like something's burning. I am using the stock heatsink and fan that came with it.

Is the CPU bad? or is the fan not big enough? Please help me out

Shutting down and a burning smell is not good.  It may mean that the heatsink is not attached correctly.  The CPU is working because it is getting hot but since there is not a good interface with the heatsink, the CPU overheats and shuts down the computer. 

Why there is no video is a different story.  Make sure all the power connections are attached and the card is firmly pushed into the slot.

Did you apply thermal paste (and the right amount of it) when you put your heatsink/fan onto the CPU? Burning smell sounds really bad...hopefully you haven't damaged anything so far, but if it were me, I'd start (gently) pulling components apart and looking for the issue.

The heatsink that came with the CPU already had paste on it. I don't get it, I firmly secured the heatsink in. It can't get any more snug. I know the CPU is the problem. I think I will try and replace it, it hasn't been 30 days since I bought it.

 

But I will try one last time and attach the heatsink again. 

CPU's rarely go bad, I doubt that's the issue unless you didn't attach the heatsink right.

Even if you didn't attach the heatsink right, I still doubt that's what the burning smell would be seeming how all the intel CPU's have a safety feature with heat. If it goes over 100c it shuts down automatically.

 I wouldn't send the CPU back until you're 100% certain that CPU is fried. Thus, pull all the components out of the PC and check them like stated. Then re-seat EVERYTHING