Touch screen selectively defective?

Today, I started to experience a problem with the manner in which my iPhone touchscreen functions. Parts of the onscreen keyboard are not responding properly. Tapping on D results in an S or an F, whilst the screen is utterly unresponsive when attempts are made to turn off the phone. The power off slider will not respond to the drag at all, and I have not found any way to force the phone to turn off without it.

The fact that the problem is very selective about when it shows up suggests to me that it is not a hardware problem. I have no problem swiping the home screen left and right from any elevation, only difficulty fully dragging the icons around the home screen. I really have no wish to take this phone to a repairman as I am a disability pensioner and thus need every cent I can retain. Can anyone suggest a way to ascertain what the problem is and how I can fix it? Thanks in advance.