I have a modern PC with wireless mouse and keyboard. I find that the very first time I use the mouse or keyboard, there is no response. The first input leaves a blank, and I have to repeat the entering of the word. Most times I double tap the mouse just to 'make it aware', and it's OK after that, but it is very annoying when I forget this, type in a password, for instance, and told that my password is wrong!
The keyboard and mouse have both charged batteries, so it's not that.
These came with the HP p6539uk PC, Intel i5, 500HDD, with Windows 7 Home Premium.