Q: Neither my wireless mouse nor the wireless keyboard will work; they have batteries

I use my computer, an iMac Intel OSX10.6.8, and do word processing and printing every day.  I came home today and neither the wireless Mouse nor the wireless Keyboard will work.  I replaced batteries, plugged in a wired mouse and keyboard, and followed instructions to set up using the set up assistant, but nothing happens.  Also, when I arrived home, my computer was Off, I had some trouble getting it to come on, and the router also was off.  I fixed those problems but the mouse and keyboard remain intractable.