1998 Ford Explorer-bad battery? turn signals?

Yesterday, my 1998 Ford Explorer had a difficult time starting, as if the battery was low on juice. I jump started it with cables to get me to work. Several times during the day, it had difficulty turning over.
This morning, I cleaned the battery cables and terminals since the negative was corroded. I made the cable ends and battery terminals clean and shiny to insure good connections. While the engine was running, I disconnected the postive cable and measured around 14 volts off of the positive cable to ground, so I assume the alternator and voltage regulator are working. However, on my way to work, I noticed the turn signals were not working. The truck still started after shutting it off, but I measured the voltage on the battery and I get around 10.5 volts, which is low.
So, do I just need a new battery and the turn signals not working are a coincidence? Could I have a bad turn signal switch or relay? I cannot determine which fuse is for the turn signals. The manual does not have the turn signals on the fuse list.
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Roger Baker wrote:

Does your Explorer have grooves on the roof running the full lentgh of the car? The grooves are about four inches from the edge on both sides. If you do, they have a tendency to leak around the top of the windshield right at the top. The water will run down the pillar post and onto the main fuseblock behind the dash. The fuse block gets rusty and screws up electrical system.. It's an easy fix, a 10mm sockat and the fuse block comes right out...
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I believe that I do. I have had leaks and I actually put some black eletrical tape along some seams at the top. I was getting water in the very back corner of the vehicle, but I wasn't sure exactly where it was leaking. So, taking out the main fuse block, which is on the side of the dash will reveal something? (Not the fuses under the hood). I will go take a look now if the tools I brought to work can handle it.
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As far as I can tell, the fuseblock seems okay. I did not get a great view inside the back though. I just noticed that the high beams do not switch on, so the multifunction switch is probably bad. I wonder how easy it is to change that.
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NEVER unhook a battery cable while the engine is running. It's a good way to destroy lots of electronics. You could do it with a generator, but don't do it with an alternator.
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