iPad 2 screen won't accept touch.

I cannot get into my iPad when the screen locks. Won't accept slider to open. I can get to my password page, but I have to pound and pound on each number until I see it is being accepted in the little white dots above. Then when I am in, I can tap on my icons and get in, but I cannot get in any further, except for the times when I pound and pound and pound and it sometimes lets me in. For instance, I can get into my email but cannot swipe up to see what's new and cannot delete.

Now, here's the fun part. When this began I was using voiceover to read to me. So now it talks to me and tells me what I am pressing and when the screen is locked. I can get in settings but not accessibility. Have done the sleep and screen button to reboot many times.