Parent dependent with expired ITIN?

No. To claim someone as a dependent, the person must have one of these: Social Security number (SSN) Individual taxpayer identification number (ITIN). 

Let's take the questions one at a time.

1. I wanted to know if she would be able to qualify as dependent or not?
   1. The rules for claiming a dependent do require an ITIN if a social security number is not available to them.
      1. Who is a qualifying dependent?
      2. Topic 857 - Who Needs an ITIN?
2. Do I need to renew here ITIN before I can claim her as a dependent?
   1. Yes

The instructions for applying for an ITIN are included here for you.  The tax return should be prepared using 999-99-9999 for the dependent (mother) without an ITIN.  When the return is printed you should remove that number and leave it blank.  The Form W-7 will be attached to the tax return and the IRS will issue the ITIN.  Expect a long period, but as long as you apply for it they will issue it and process the tax return.

• How do I get an Individual Taxpayer Identification Number?
  How do I file with a W-7?