Friv was my fucking drug when I was a kid, I spent hours and hours playing on that page on my father's computer, then I grew up and I went to Happy Wheels, I had a childhood full of video games.
To my best knowledge, I believe the game is strike force kitty. I found this game on Friv awhile ago.
SOLVED for myself.. The site I was thinking of was friv.com, not fipl, but definitely four letter URL containing the letters F and I. The background is purple, not blue.
I found it by searching for something similar to OMGPOP, and voila! Third in the list after Kongregate and Cafe was Friv.
My thanks to anyone who tried to find it for me.