Windows 7: BSOD while opening certain websites.

Hello! I am using my Toshiba Satellite L455D-S5976.
I'm using Windows Home Premium 64bit version, I'm assuming it's the original? I have no idea. I'm a little lost when it comes to computers and their specs etc.
I'm not sure how old the hardware is, it was given to me by my father about a week ago (it was used previously.)

However when I try to open websites (I/E: Tumblr) I get a BSOD with this error: BAD_POOL_HEADER
I've also had it happen doing other things but I can't recall exactly what. Sorry. ):

I've read that it has something to do with hardware not being installed correctly.. but I don't know.
Here's the info, dumps attached:

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Problem signature:
Problem Event Name: BlueScreen
OS Version: 6.1.7601.2.1.0.768.3
Locale ID: 1033

Additional information about the problem:
BCCode: 19
BCP1: 0000000000000020
BCP2: FFFFF80000BA21E0
BCP3: FFFFF80000BA2BB0
BCP4: 00000000049D9A02
OS Version: 6_1_7601
Service Pack: 1_0
Product: 768_1

SOFTWARE

There seems to be a problem with your Windows installation. Please follow the Windows Genuine and Activation Issue Posting Instructions. Post the results in your next post; do not start a new thread.

You do not seem to have an anti-virus running. What AV are you currently using?

DRIVERS

The dumps all point to RTL8187Se.sys, a driver associated with Realtek Wi-Fi. From the below link please download and install the latest BIOS and WiFi drivers (2nd and 3rd downloads).
Toshiba Satellite L455D-S5976 Drivers

I went to install the latest BIOs and followed the instructions EXACTLY. Now my computer blue screens upon start up. I've tried system restores and repairs. Nothing is working.
The blue screen flashed briefly before the whole computer restarts again.
F8 > Disable restart upon crash and this is what the error reads:

*** STOP: 0x0000007B (0xFFFFF880009BB928, 0xFFFFFFFFC0000034, 0x0000000000000000, 0x0000000000000000)

Run a Repair Install. It should fix your current version and Windows 7 but preserve your data, programs, user accounts etc.

Can you boot into safe mode?

I can't boot into safe mode. Do you think just wiping it clean and re installing windows would work?

It would work if it's not a hardware problem but we can't know that for sure yet. You will also lose all of your data.

For now just try the Repair Install before we talk about the clean install.