I've got a cordless keyboard and mouse, I have to press the red buttons on them in a certain order to start it up, probably something like that on yours.
try clicking both buttons at the same time and what computer do you have if its too old it might not read USBs my old old old old pc was a windows me and it didnt read pendrives so idk and i dont even think my windows 95 from wen i was like 5 even had a usb port...
Sounds like battery problems to me, never do wireless while gaming, it will leave you in a situation where it will go dead in a middle and no way out of it