A little wider reading would have taught you that your TF charger outputs at both 5v & ~15v. The connections in the cable, charger & device determine which is used. So, your charger and cable will charge your phone at 5v - just not your TF at 15v.
The data wires are different to the charging wires - each single cable contains a whole lot of small wires, y'know.
Buy a new charger &/or cable - or alternatively give the TF300 to a charity and buy something a little more robust/up to date. Your money - your choice.