Pleos don't require a memory card to work, that's just to program/reprogram/run skits/check status.. etc.. It should just require a charged battery to run.
If it won't turn on, I agree.. sounds like the battery.. talk to RedWoodsMama, on this forum, about an 'egg battery' she sells them. They work better for the older models.. work for longer and are much better than those old green batteries that have been sitting around for so long. (The pleos even move a bit faster)
For now you can just try to charge the battery, some folks have had some luck with putting the battery in the charger then taking it out and putting it back in.. kind of babying it and milking it to get it to charge.. if you an get even a little bit of charge in it, the Pleo should run. If that wont work it could even be the charger or cord that's failing, again, that other battery is awesome, I have one for each of my older model Pleos and I love them..
Best of luck, let us know how it goes.. !
- Sarah