I received a 1099-DIV with, lets say, $70.00 in box 1a and box 1b.
I still hold the stock which has a "paper loss".
Do I still have to report the amount in box 1a.
And what can be done with box 1b?

Thank you for any help with this matter. I always do my own taxes (the old school way), and this is just something new for me.

You will report ordinary dividend on schedule B (Form 1040). Ordinary dividends are taxed as ordinary income, they're just added on to the rest of your income.
Qualified dividends represent a payout of capital gains and are taxed as long-term capital gains.