Chosen Solution

I have rugged iphone 5 which is mportant for me. For the past few days i noticed the screen of my phone was bulging out, so i just decided to open it.I noticed the battery to be swelled up , i kept everything back in position and bought a battery from a nearby technical shop($22).and i just removed the older one the new one in its place.After i fixed the battery i tried to switch it on without the screen the processor portion was warming up so i thought the battery was okay and fixed the digitiser but after that when i tried to turn on my phone it was not turning on and i tried to charge still of no use.If someone out there knows the cause of this problem pls help me

Please tell me you did not pry against the board (between the board and the battery) while trying to remove the battery. In which case you will need board level repair to get it back to a working condition. Otherwise, like @benjamen50 said, in case you unplugged the screens without disconnecting the battery, you may have damaged the display circuit (specifically and most likely the backlight). To verify, connect the iPhone to iTunes, is it detected?

Did you make sure battery was unplugged when plugging or unplugging screen cables?