I can't send Bitcoins with Electrum, because it won't recognise the other address as valid, while i know for certain it is.
Are you sure that the address is valid? Are you absolutely sure that you are entering it in correctly? If you enter the address on a block explorer, does it give you an error or give you a page with info about the address?
I heard this could be the case, because i still use an old address, that starts with 1. Could this be the case? If it is, what can i do now?
No, those addresses are not old and are still used. That is not your problem.