Steaks look light brown aren't charing
I have made steak with a stainless steel pan and I haven't any issues achieving browning. Yes, a cast iron pan would be better, but a good stainless steel pan can work too.

Here is my technique (I am also using gas):


Heat pan without anything in it.
When it's hot enough, I add the oil to coat the bottom.
Then add the meat to sear both sides. I usually finish the whole thing in the oven. (Make sure to check your pan is oven safe).
Depending on the size of the steak, sometimes I just finish it there, sometimes I finish it in the oven.


Other notes:


Make sure the pan is hot enough
If your stainless pan is really thin, you may still have an issue. If this is the case you may want to invest in another pan. Cast iron pans last for ever and can be had for cheap.
Make sure your steaks are at room temperature. Take them out of the fridge 30 minutes prior to cooking.
Remove any moisture from the surface prior to cooking. You don't want to have to heat the water first (steaming the meat), and then browning. You want it to brown right away.


Edit: to add the info suggested by jalbee and Henrik