i5 4770k with corsair h80i. But only 600w psu...

Solution
exactly, you'd want a higher quality PSU, preferably along these lines;

PSU; Corsair/Antec/XFX/Seasonic with a minimum of 80+ Bronze and at least 5 years warranty 600-650W.
yes, you can but what is your graphics card? if you have a GTX 780/R9 290+ Card then you are fine but depends on the quality of the PSU.

If you have a GTX 770/R9 280X or below card then yes.


What PSU is it? A poor quality 600w PSU may only deliver 500Watt and have a never stable power delivery whilst a 550 watt high quality has a much better, stable output.
 


My psu is a KRAFT 600W dont know what certification. And i got a gtx 770 (msis) 2gb VRAM