the pertinent posts I have repeated above ^^ .
also when inserting the new cable make sure you have tapped the small lever enough times so you are in the highest gear i.e. would be small cog (if this is the shifter for the rear derailleur) as the hole to thread the cable thru only appears then. If you have done this on the hole is still not visible, there must still be some frayed thread stuck in the shifter mechanism. A blast of air (compressed or minipump) is sometimes your friend here along with tweezers / gravity and shifting up and down until all bits fall out thru the cover you have removed.
Obviously its much better not to let your cable fray until it snaps, but having been there and done that, patience and working methodically will get it sorted eventually.
only remove that cover and peel the hood back, do not attempted to remove any more shifter parts, shimano shifters are designed not be be properly serviceable or re-assemble-able!!!!