Grout does nothing to waterproof your shower. In a conventionally built shower, the combination of a liner and some type of waterproofing on the walls keeps water running toward the drain.
It's hard to say exactly what is causing the problem until the shower is torn out to some degree. You can be sure that you'll have to take out the floor and wall tile up to about 6" above the level of the step. Since a patch job never looks as good as the original job, it's not a procedure that I recommend, but it can be done.
Most of the time, a failure in a tile shower is caused by an improperly installed liner. There are a number of things that could be done incorrectly, and any one of them could be the cause of failure.
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The top ten reasons to procrastinate:
1.