How far to upgrade laptop memory? - upgrade hits BSOD!

[Deleted User]

I couldn't sleep until I got some proper references to the above to confirm what I was thinking in my previous post, I now have.
 
1. Your laptop uses the Intel HM55 chipset: https://www.dell.com/community/Laptops-General-Read-Only/DELL-Inspiron-1564-RAM-Upgrade/td-p/4569059

2. The HM55 chipset supports a maximum size of 256Mx8bit memory chips on the module - so for a 4GB module that needs 16x256M chips so it does need to be a 16 chip - ie 2Rx16 https://community.intel.com/t5/Intel-Desktop-Boards/Intel-HM55-Express-Chipset-with-Kingston-RAM-8GB-1600-MHz/td-p/290275

You have bought 8 chip RAM 4GB modules 8x512Mx8bit - they are not supported

So it is the chip density that is the problem on the RAM you bought, it is not compatible with the chipset. Single / dual rank is related to this - single rank have fewer chips, combo of both issues. Make sure you buy 2Rx16 4GB chips instead - ie  the exact models recommended by the compatibility checking websites - not just ones with similar specs.

HereToday

OP...try to listen. Send the RAM back and buy a single 2GB module for £1: https://uk.webuy.com/product-detail?id=200pinsmbpcpn&categoryName=memory-laptop-ddr3&superCatName=computing&title=2-gb-pc8500-ddr3-1066mhz-204-pin-memory

and spend the rest on a solid state drive. You seem to have got it into your head that you want this RAM upgrade no matter what.
4 GB of RAM and a solid state drive will be much faster than with 8 GB of RAM and a HDD. Much faster. You are wasting your money on nonsense.
The SSD you can use again in any new device. The RAM will be fit for the bin. So don't spend any money on RAM. Spend it on a good quality SSD. How many times do you need to be told before it sinks in?