Is Intel Core i7-4790 CPU @ 3.60GHz compatible with Hynix RAM of "1GB 2Rx8 PC2-5300U-555-12" ? Or, is there some severe issues when these two devices co-exist in one machine ?
You can find the memory specifications for your processor here:
https://ark.intel.com/products/80806/Intel-Core-i7-4790-Processor-8M-Cache-up-to-4_00-GHz Intel® Core™ i7-4790 Processor (8M Cache, up to 4.00 GHz) Product Specifications
Specifically, the processor supports DDR3-1333/1600, DDR3L-1333/1600 @ 1.5V
You should also check what your motherboard supports.
It is the speed, in MHz, at which the memory operates; 1333MHz or 1600MHz.
For more information on memory, look here: http://www.crucial.com/usa/en/support-memory-speeds-compatability RAM Memory Speeds & Compatibility | Crucial.com
The above link is provided only for your convenience.