Below are two webkit based exploits for the PS3, these will allow you to flash CFW after running these two exploits.
First step to identifying which of the two links you want is to identify which PS3 you have!
Click here to identify which model you have.
When looking at the back of the PHAT PS3, does it say "Axx/Bxx/Cxx/Exx/Gxx"? if so, you have a Nand PS3!
If you have anything else on a PHAT PS3, you have a NOR PS3! If you have a slim (20xx ONLY!!!) PS3 you have a NOR PS3!

Make sure that you have the file on my site linked here,
at the root of your USB Drive in the slot closest to your Blu Ray drive on the front!

Make sure your browser has no other tabs open! Don't want to screw up memory.

Ready to go? Good luck!!

Click on the button and wait for PS3 to power down. DO NOT STOP THE PROCESS ONCE STARTED!!
Once PS3 has powered down, reboot console and install CFW matching OFW version. If installing through XMB does not work, boot to recovery and install.

Here's a link to a 4.82 CFW. Here's what I use.

Click this for NAND:
NAND

Click this for NOR:
NOR