Try with 1 stick ram, in each slot,, also switch the ram sticks, remove battery and power cable always when you touch ANY motherboard connector or ram slot. Just test in between with power cable then plug off.
You can still try reflash bios by this method, download bios with your exact model and follow this guide :
View: https://www.youtube.com/watch?v=OkadkPyGjY4
Also test to boot the motherboard "barebone" remove everything including power button cable, just leave cpu in place and ram. Then remove cmos battery too. After that plugin power cable it should boot on without power button, if you get picture then faulty component somewhere.
Its usually the amd northbridge failing on these dv4-5-6 series laptops so you wont get picture with egpu.
Remove processor from the motherboard and tapes near the ati radeon gpu chip and northbridge chip, reflow 150c with heatgun, if you get picture then problem inside the cheap "fixed" by heat expansion. Not by cracked solder.
If it works , might be a day up to a year but thats unlikely, atleast if you dont do higher temperature reflow. Its not really considered a fix since the chip is about to fail.
Real fix is new motherboard, you can fit many other dv6 motherbords in the "case", some with slight modification. Thing is there is few chipsets which are more failsafe, i can tell more on these if you decide to get new mobo.