Dell Inspiron 3537 sometimes boots,most of times not

Hi to all!
One day I shut down my Dell Inspiron 15 3537 (running on Win 7 Ultimate 64 bit) via start>shut down.After a few minutes I turned the laptop on but it would not boot!It showed black screen and continued to shut down or it turned on but there was only black screen,there was a noise from the fans which worked,and only the power light was on,the hdd light was off.After a couple of times I somehow managed to turn it on and I formatted the hdd and reinstalled the windows because of thinking that the problem is caused due to a virus.I installed the windows and all of the drivers and I updated all of them to the latest versions.Everything seemed to be fine until I shut it down via start>shut down!The laptop wouldn't boot!After 10 or more tries I managed to turn it on but it gave me a bsod:stop 0x0000001E.After that I made a registry repair with the win 7 dvd and it showed me this:the following startup options will be repaired name:windows boot manager and the following atartup options will be added:windows recovery enviroment,after that I restarted the laptop and I made all the possible hardware tests I know including the dell hardware online diagnostics, then the dell onboard diagnostics ,then the hdd s.m.a.r.t scan and all of the hardware components passed all of the tests!The tests didn't found problems with the motherboard,hdd,video card,monitor etc.And I founded that when the laptop boots (after 100 tries to turn it on!) it works without problem,once I left it to work for 12 or more hours and it worked without problem!But after I turn it off via start.>shut down I can't turn it on normally,it usually takes 50 or more times pressing the power button while it shuts down imeddiately or restarts itself and shuts down again,or it turns off but with blank screen,with only power light on and hdd light off and fans working....Please help me !I want to repair it myself at home!I got borred to press the power button over 50 times to turn it on ,or sometimes I must do a hard reset while pressing and holding the power button for 60 sec and then put the battery inPlease help me!.Any help would be appreciated!Thanks in advance!Best regards!
p.s I do apologize for my bad English
 
You've been incredibly thorough. Is it possible that the power button itself is the problem here?
 
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