I have yet to see a PRAM battery fail on an iMac since the G5's. Look for other things unless your date and time are not holding and your printer is dropping off line.
Sorry I am getting old and forgetful:
iMac (27-inch): AMD Radeon 6970M Video Card Replacement Program
Apple has determined that some AMD Radeon HD 6970M video cards used in 27-inch iMac computers with 3.1GHz quad-core Intel Core i5 or 3.4GHz quad-core Intel Core i7 processors may fail, causing the computer’s display to appear distorted, white or blue with vertical lines, or to turn black. iMac computers with affected video cards were sold between May 2011 and October 2012.
The ethernet cables do get old and fail, try replacing it.