BSOD after upgrading RAM

This is the only RAM match I found, GB Ram Technologies on Ebay site.
Return the RAM for refund if you are still within the 30 days money back period.
There are a few reasons why this RAM may not be working, one being it is just bad RAM, size of memory chips on the card, not much info on that site to use in determining what it is exactly.

4GB Sony Vaio VGC-LT15E VGC-LT16E VGC-LT18E Memory RAM
Item specifics
Condition: New: A brand-new, unused, unopened, undamaged item in its original packaging (where packaging is ... Read moreabout the condition Number of Pins: 200
Capacity: 4GB Kit (2 x 2GB) Speed: PC2-5300 at 667MHz
Warranty: Lifetime Memory Type: DDR2

Recommend to get your RAM from one of the major vendors, Crucial guarantees their RAM to work with many OEMs including Sony.

Crucial® Memory Advisor results for the Sony VAIO VGC-LT18E Desktop/PC.

4GB kit (2GBx2)
DDR2 PC2-5300 • CL=5 • Unbuffered • NON-ECC • DDR2-667 • 1.8V • 256Meg x 64 • • Part #: CT742936

For $9 more, you'll get good quality RAM.

The main drive is labeled as Vista. That doesn't show which version is on it however since you can change the volume label to anything.

After a clean install of any version of Windows you will see C "local disk". To know which version you are running you can right click on the Computer icon if set to shown on the desktop or go into the Control Panel>System for the information displayed there.

As for backing up all of your files do you have an external hard drive or usb enclosure to put a drive in? If the laptop has room as many of the larger models will have a second spot to add a second HD in would take care of backing things up. For simply using the upgrade option without wiping C entirely the Windows installer will simply pack things up into the Windows.old folder.

When not having an external drive available an external enclosure allows you to transfer files from the main drive onto another machine for temp storage in order to see a complete wipe and fresh start. Also if you have an external drive but can't boot into Windows which seems to be the case you can try booting from a live Linux cd(or live flash drive) in order use the other OS's file browser to copy and paste files over to the external drive as a last resort.

There are several but limited options when not able to stay booted in Windows in order to see your files backed up. And the need for some place to back them up to is also needed as well.

Meanwhile you will want to look at what Dave76 found for your memory situation since getting the hardware straightened out might just save you the need for another Windows install. I know what it's like needing to go back out and buy new ram.

When first getting the present build together the recommended memory list for Gigabyte showed the OCZ Gold memory was suitable except the board backclocked the 1.9v memory down from 1600mhz to 1066mhz! The board itself took 1.5v according to the user manual when first having a chance to go over that!
(fortunately the OCZ memory found a new home on another 7 HP case in the works! )