first I strongly, and can't say enough STRONGLY, advise you don't continue to attempt to turn the device on. I would take it to a reputable repair store and have them run a professional cleaning on it. Make sure they use an ultrasonic cleaner and remove any necessary shielding over board components.
You basically want to clean off any left over minerals from the liquid that has been left on the board.
Many times a cleaning itself will work but in the case it doesn't and you have one or multiple shorts you will need a board level specialist to look at it.
Also I wouldn't wait as there could still be liquid sitting in the device waiting to cause more damage.
If personal data is your biggest concern be very picky who you let touch your phone. Just because they operate a store doesn't mean they're good at what they do. I'd check out the business's online reviews prior to letting them touch the device. Hope this helps a little.