The fan and light both work, but both of the indicators don't light? Did the lights both go out at exactly the same time? The more clear and precise you can be about describing the symptoms to the customer service person, the more likely you'll to get help. By phone is probably best.

It's easy to check to see for yourself if all the wires are plugged into back of each switch. Just remove the front square grates and shine a flashlight in there. There are supposed to be three wires in each switch: A Black, a White, and a Blue.

If they did both go out simultaneously, but the fan and light still both operate, the problem might be the white wires as they complete the circuits that allow the little blue leds to light up.

If the problem is internal to the switches, and you're handy, have them send you a couple and you can install them yourself. It's not rocket science. Just make sure the stove is unplugged and that you be certain the wires are plugged into the new switch exactly like they were in your old one.

The burners and front inner faceplate need to be removed. It looks to be all the same kind of Phillips screws. The switches pop out by pushing from behind while squeezing the top and bottom to release the plastic retainers. Once out in front, it's easy to unplug the three wires, plug them into the new switch in exactly the same locations, and simply click the switch back in place.

Don't be discouraged.
The least likely explanation is that Blue Star is exempted from covering led light failure somewhere deep in their warranty if you want to dig around, or more likely they consider it so minor in the overall use of your appliance (which it is) that they are waiting to see if something more serious also turns up before the warranty is finished. That way labor expense wouldn't look so big and bad when compared to a few cheap parts .
That doesn't let them off the hook and you should continue to insist on the repair they owe you especially as warranty expiration draws closer.
In the meantime, if you don't have someone around who has one and who knows how to use it, you might want to acquire an "analog multimeter" like the one in the link which are usually found at places like PepBoys, etc. at bargain prices. Be sure to get this one, not the digital readout type. Or you could buy one of each if you want to.
Always good to try to narrow down the problem. And it helps everyone.

Here is a link that might be useful: Analog Multimeter YX-1000A