My IPhone4 keeps buzzing randomly and now it wont even charge

Question

My IPhone4 keeps buzzing randomly and now it wont even charge !! Please "HELP"
Info:
IPhone 4
Version : 5.1
I was having this problem with the vibration IPhone keeps vibrating randomly with no notification don't know what's the problem with it !!
And currently when I tried to charge it it wont charge I tried to do some research about this issue and have read some of the same problem
here in the forum with same issue and done almost everything changed the cable , core , usb did the hard reset still nothing !!!
Any idea would be appreciated . Thanks
Updated:
I discovered that its not a battery issue
The reason is that it's chargeable while the phone is switched off completely !
after a while you can see the battery charge is full 100%
but when it's switched on the phone wont charge or recognized
the cable from wall charger or usb so I the ITunes won't sync or see the device !
I think its something with the software ! 
I tried to update to IOS 5.1.1  but after downloading
it wont install the new update I got this message;
"Unable to Install Update"
An error occurred installing IOS 5.1.1
So that only chance which I think it might hwlp solving the problem is dead now
I really have no idea what to do other than taking this phone to Apple 
:If you have similar issue you can write here or you can check the following post
https://plus.google.com/u/0/109937970144676369628/posts/Hrv43wnzREE
keywords:
IPhone keeps buzzing , IPhone4 keeps buzzing
IPhone4 keeps vibrating , IPhone wont charge
An error occurred installing , Unable to Install Update , 
IPhone wont connect to iTunes .

Answer 1

UPDATE: 2
My IPhone4 keeps buzzing randomly and now it wont even charge !! Please "HELP"
https://plus.google.com/u/0/109937970144676369628/posts/CrAi9u9PZz7
https://plus.google.com/u/0/109937970144676369628/posts/Hrv43wnzREE
https://plus.google.com/u/0/109937970144676369628/posts/a2TeUdCHoQs
OK folks I started my deep research about this issue ( MY problem )
Don't know if some one out there is even got similar issue
The battery is charging well while my phone is switched off so last night
my Iphone runs out of charge completely 0% so I plugged the cable
and switch it on after a while and all the sudden it shows that the battery
is charging while its switched on !!
If you want to do this you have to plug the charging cable first then turn off
your Iphone and wait for a while then  turn it back on ( sipmle off ) no need
for the (Hard) Reset or recovery mode / DFU mode .
Just as a normal way to of switching off your Iphone by
Holding down the sleep/wake button at the top right-hand corner of the iPhone for a few seconds. 
This will bring up a screen asking you to run the slider across the screen to turn off the iPhone.
Wait few seconds and repeat that with holding that same sleep/wake button at the top right-hand corner for like a Sec and it will turn on , Then you can
see that your phone is charging while its on !
If you unplug your charging cable this will ruin the whole plan and if you
you plug it again it wont show anything and will not be able to charge
while its on and you have to repeat that procedure.
Now we are sure that out Dock and Charging Port and battery are working fine , So whats the problem here and why my PC wont detect my Iphone ??
Well I assume its from a part called ( PMU IC ) Power Management Unit IC
http://www.buyforapple.com/product_images/j/iphone4_power_management_un__72870.j pg
Check this out :
http://youtu.be/MJPKuLy7XQQ
So I think my main problem is from that tiny part that makes all that
problem I have now so I have to replace it first just to make sure before
replacing any other parts so this is the start I hope this was the problem
that caused all this !!!
If you have any similar issue to mine I really appreciate any advice ,
suggestions regarding this matter .
Thanks for reading
Have a great time