Hi and welcome to ExTS
I assume that the OS is Win 7 ( from your profile ) Could you confirm this please?
Also - let us know the make and model number of the laptop ( this may help later )
It is a possibility that dust has built up inside the case.
The usual first step is to get a can of compressed air ( any computer shop even motor factors ) and, using short blasts, spray through the vents.
This is best done outside.
Just picking up your machine and it blue screens suggests a bad connection.
Try taking the battery out and running on just the power-adapter.
Also try just the battery without the mains adapter connected.
If the RAM is accessible ( usually under a panel in the base ) take this out and replace.
You could also try these one at a time.
If you hold the keyboard firmly on a table and move the screen backwards and forwards - does it blue screen doing this ?
Let us know the results of the above.