Dell Studio 1558 - No post/boot

try reseating the RAM actually make sure it is properly inserted then if it still doesn't work try with one stick

This sounds like it could be an overheating issue. Some manufacturers use a cheap thermal paste on their processors. If you are dealing with a computer this should be an easy fix but if you are dealing with a laptop then it is much more involved. Go to Youtube and research replacing or removing heat sink. You wont be replacing the heat sink but the procedure is the same except you will need to clean the old paste off your heat sink before you apply more. Don't go crazy with the paste, a little goes a long way, all you are doing with the thermal paste is ensuring full contact between the processor and the heat sink with no air gaps.

no dear, there is no bypass jumper in it, go for the solution dell suggested for you

seems like your screen have some dead pixels. the only solution is replacing the screen. ita a hardware problem not software.

Well since you've done System Recovery which deletes all your data, why not just reinstall windows?

Hardware failure, most likely in the motherboard. Take the laptop to a repair shop for an in-depth testing. Beware, the repair will be expensive.

sound like your core is geting hot is your fan working is so try cleaning it with small birst of air plus check your bios settings..if not overheating try factory settings...

basic troubleshooting steps include the following:
Ensure that the BIOS, the Notebook System Software and the Video/Audio drivers are all most current available.
All can be downloaded here:
http://support.dell.com/support/downloads/driverslist.aspx?c=us&cs=19&l=en&s=dhs&os=WW1&osl=en&SystemID=STUDIO1558&catid=-1&impid=-1
If issues persist, run diagnostics, see if a hardware failure is detected (Power button while holding Fn button should initiated diags)
If that still doesn't help, you can try the system with the RAM modules individually (Often a crash issue is isolated to one RAM module or the other, regardless of DIAGS results)
if issues still persist and no hardware has been IDd as a problem, then run Malwarebytes from download.cnet.com

Here is the Dell service manual page where it shows the disassembling of the Dell 1558.
You will have to remove the DVD module to eject the DVD
Procedural steps are on this page site.

http://support.dell.com/support/edocs/systems/studio1558/en/index.htm

Check the BIOS for PC Health settings. It is possible that you have put a low value for "Critical Temperature", which makes the Laptop to turn off.