Power Issues

I have had issues with battery corrosion over the last
couple years and a few times couldn't start the car. I had
to clean the cables several times. About a month ago, I
started hearing a whining noise and then it seemed like I
was losing power and the battery light came on. Drove
straight to the shop, and was told I needed a new
alternator. I paid $500 for a new alternator only to notice
the next day that my battery light would intermittently
flicker, only for a few seconds. It never did this before the
alternator was replaced. I drove it back to the shop, they
looked it over and said everything looked fine and it might
just be a glitch. Over the next few weeks, I noticed that
every once in a while my car seemed to have a hard time
starting. And now over the last week or so, it randomly
won't start at all. When it doesn't start, the lights are all
still working fine, I wait a few min and then it starts just
fine. It's a very random and intermittent problem. I took it
back to the same shop and they said they thought it was
a loose battery connector, so they charged me for that
and replaced it. I'm still having the same issues. I'm a new
mom on a super limited budget, so I'm getting really
frustrated. My gut says it's the bad battery cables again,
since I've had so many issues in the past. But, they keep
saying they can't see corrosion. Is it possible the
corrosion is further down the cable where they can't see
it? I've already paid a lot of money that I don't have for an
unresolved issue. Any pointers or advice would be so
much appreciated. Thank you!!