How can I access pipes in my cement shower in an old home?
There is no secret to getting to a cement shower.  I just took one out of my master bath and if I didn't have a lot of reasons for doing it then I would have left it.  They are great if done right and you can basically retile them infinitely...  

So first you should try to get to your valve from the side or back.  If that won't work you will have have to cut out a piece of the cement.  I would in no way take out the whole shower.  Just a cutout where you need to reach the plumbing. 

Next you have to get rid of all the tile to figure out what condition concrete is in.  Most of the time (95%) it is in great shape.  It may need to be slightly patched or smoothed out then waterproofed.  This is very easy.  Really the only thing that go "bad" with these showers is the floor.  Sometimes you will have to make a new base because of extensive water damage - this can be a big project. 

But there is nothing wrong with a concrete shower.  And the mold, grime, and mildew is probably a case of poor tile install or old tile not being grouted as you have said.  If things are in good condition under just retile.  If the pan is in good condition then this is a no brainer.  Post pictures if you are thinking about demoing the whole thing (might be talking about couple thousand pounds of cement for a big shower).