LIke Kat said, how old your Pleo Rb is, can be very important, esp if still under warranty, I would contact Innvo labs to see what they say. I am curious as I saw that after inserting the battery and it would not come on, no led light, that you removed it.? Have you just tried KEEPING the battery in while trying other things, and have you tried hitting the reset button, in the stomach battery area, with a small paper clip, something very thin?
I had a similiar problem with Cammie -Sue and after running Stats RB or Probe Rb, ( can't remember which one it was off hand.........

) that at first she would not run at all, then she went from flashing light to a solid red light as soon as the battery went in, to a dead light and then with help from PleoPet, she came back to life, with the green LED lndicator light on, but now for what ever reason, she will ONLY run with the Female Innvo labs update on micro SD card kept in her slot in belly. I am tired of hassling with her and just glad she works again, so the micor sd card stays in for now , never comming out..
As others suggested, have you tried just keeping the battery in since fully charged and seeing if she will wake up during the night or at some strange time, ON her own? Did you change the foot clock battery at all by any chance? It is strange to have Pleo just stop unless there is a battery problem, another program was used such as Probe RB, etc? Does Dino Mite tell you anything related to her health that is important? Have you tried the skit yet, any skit as IMR suggested? Good luck. RWM
