Oh so looks like you got the heating element burned may also be an electric contact that disconnected or a switch issue , if you hear a "prrrrr" sound it is the pump that is working but heating element steam producer does not work.... I do not know very well the type of iron and not sure if it is a thing you could get cheaply fixed in a repair center, you could just ask a quote....
I'm mostly used to see and I know more about pressure boiler mechanicals, but you may try to open it to see if maybe some wires got disconnected.
You're right bigger pressure types can take till 10 minutes to get hot, my new very basic one just takes 3 mins...it is a compact type and hold almost 1 lt of water that last for almost 1 hour of ironing....but yes I can say they last longer and produce more steam and works better, the fact they last longer it is for their nature being just a steam chamber with an element and a heat sensor and a solenoid that opens when you press the steam button ,very durable mechanics, while pump things are more usual to get broken more delicate and not as functional even if more convenient on the refill aspect.....
If it is the fact of waiting for refill the fact of bothers you:
Actually you may implement a trick, to skip cooling fase and so pressure dejection before re-filling, this is possible with some models having solenoid working even with boiler element switch turned off (almost all pressure irons now do this), mine does as polti did and I could actually avoid waiting as after I turn off heating in the chamber by keeping pressing the steam button I can discharge the pressure in the chamber within some seconds and refill once the pressure got discharged.....it is not suggested to do it in manuals for safety but you could do that....
Where to get it repaired:
I cannot really know if there's an authorized or "used-to" Rowenta brand repairs center in SF area, but you may try to write or call Rowenta Customer care on their website to ask for repair centers near or in SF, they should have a toll-free number I think as every respectable company.......
Here is a pic of what a pump steam generator looks like:
