A discrete graphics card is installed via PCIe slot, not soldered onto the motherboard.  An integrated graphics, only available on certain processor and is built-in the CPU, which is located underneath a big heatsink with fan. If you are able to see certain damage, cracked on the motherboard, then regardless what the part is, that motherboard is bad.  No further troubleshooting is needed. If you want to replace another (30 usd) motherboard to salvage and make use of other parts, or you want to learn and tinker with repairing your computer, it's better to get a whole (50 usd) barebone system, which contains a motherboard, power supply, heatsink, and the case itself.   
So currently I am troubleshooting workstation Precision Tower 3620 and it won't power on AT ALL. First we thought that PSU is the reason of all of that so we've installed a new one PSU but it didn't power on with another PSU anyways. When I press that test button on the back of the PSU LED blinks and fans spin for a sec. I am writing here because I am not really great at troubleshooting and do know very little about all of this. Also I noticed on the Internet if that's a system board failure, on front head panel LED would at least blink but when I press the power button it is not blinking at all. Could that be front panel failure or something?
Precision Tower 3620 doesn't power on.