Screen Replacement Problems and Buttons Not Working

I dropped my iPad mini over a year ago and smashed the digitizer display. i replaced this and then the lcd screen broke too so i replaced that but i did this without disconnecting the battery as i did not know that i needed to disconnect it. after doing this, the screen would not come on but the iPad would make sounds e.g. when it was charging.

i read up about the problem and found that i may have blown a fuse on my board for the backlight. so i just left the iPad on a shelf and didn't use it for several months. i picked it up today and plugged it in to see if anything happened and the battery charging icon came on the screen. now the screen works and sound works.

except, my digitizer is not stuck to the ipad but is connected and when i touch certain parts of the screen, other parts interract or nothing happens at all. also, the home and power button now seem not to work but the power button only works when it is held down to power off the device.

has anybody had this problem before or know how to solve this. someone wreckons that they could repair it for £45 but it seems too good to be true.

thanks