i have a 28mAh power brick capable of charging my laptop when charged. I bought a 28W solar panel which outputs 5V over usb capable of charging ipads etc, however when i connected it to power brick's input it couldnt charge it (or at least charging light didnt come on) Its only then i realised power brick is running off 15-19V 2A mains charger. Is it possible to step up my solar panel to this voltage and trickle charge the power brick at all?
You didn't provide enough details so I can't say for sure but it's possible to step up the voltage but it will not help you that you for a simple reason:
your device runs on 15-19 volts 2 amps which means it runs on 30-38 watts but the solar panels output is 28 watts , so if your power brick doesn't work on less than 2 amps or a voltage below 15 volts then it won't work again.
Yes, it is possible. You need a boost or step-up converter. A step-up converter can increase the voltage (but the power VI is constant.)