Why skype doesn't download into my iPhone ?

I have Verizon Wireless iPhone 5S.

From home screen I click on App Store.  I search for Skype.  I click on GET.  Then, I click on INSTALL.
I enter my Apple ID and Password.  System displays the following:

"Your Apple ID or password is incorrect."

I have changed my password few times and also created new  password.

Previously, this was my daughter's phone.  Does the system only recognize her Apple ID or her email address ?

What might be the problem ?
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The phone needs to be disassociated from your daughter's account.  Should have done this before she transferred the phone to you.

Tap Settings > iCloud, scroll down, and tap Sign Out. In iOS 7 or earlier, tap Delete Account.
Tap Sign Out again, tap Delete from My iPhone, then enter your (daughter's) password.

Go to Settings > General > Reset, then tap Erase All Content and Settings.

This will completely erase your daughter's content and settings from your device, including any credit or debit cards she added for Apple Pay and any photos, contacts, music, or apps. It will also turn off iCloud, iMessage, FaceTime, Game Center, and other services.

If you're using iOS 7 or later and she had Find My iPhone turned on, her Apple ID and password will be required. After you provide her password, the device will be erased and removed from her account so that you can activate it on yours.

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naseeamAuthor Commented:
I performed the erase operation.  

When I try to install Skype on my iphone, it prompts me for my Apple id and password.  I enter the information.
Response from iphone is as follows:

"Cannot connect to iTunes Store."  

Did I not set something after the erase ?    I haven't setup my email yet.  Would that have anything to do with this ?
Is it able to connect to the Internet?
Are you connected via wifi or cellular?

And *did you do the step, described above, of deleting the iCloud account, using your daughter's password*?
naseeamAuthor Commented:
Extremely happy with the solution provided by expert.  Verizon and Apple spent 3 hrs and couldn't solve it.
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