Make sure you've left you phone to charge for a few hours, because if the battery isn't charged enough, it won't turn on at all. If that doesn't work, something may be wrong with your battery and you'll probably need to replace it with a new one.

Changes are that it's a lost cause by now, but you could try to dry everything out in a tub of rice. The rice absorbs any extra moisture that might be still in the phone. Make sure you don't have any sand stuck in it as well I guess. You can use canned air to blow that stuff out.

Inside the headphone jack is usually some kind of trigger or sensor so the phone knows that headphones are plugged in. If the headphone jack gets dirty, this trigger may not un-press so the phone will think there are still headphones plugged in. Try cleaning out the jack with some compressed air, or if that doesn't work, use some isopropyl alcohol on a q-tip or toothbrush. Make sure you let any alcohol dry off before plugging anything into the jack. Also make sure the phone is off before you go poking around with liquids in your phone!