I turned my iphone off when visiting the doctor's surgery and now it won't turn back on. It had 73% battery left and I have tried connecting it to my computer with USB but nothing happens. I have taken out and replaced the sim card too. Any suggestions

Try resetting it:

Press the Sleep/Wake button & Home button at the same time, keep pressing until you see the Apple logo, then release.

If wjosten's tip doesn't work try plugging it into a USB charger (not through your computer), wait about 30 seconds and it should come on. If it doesn't remove the cord from the phone and keep trying this. I've had this same issue and found a combination of the reset & charging cable tends to work. Sometimes it takes about 5 minutes for the phone to respond.

Best of luck.