If you can't come up with the registered names, and numbers of the goats, you can't register their kids. If you didn't own or have bills of sales of the grandparents that were registered, the dams and sire, you can't register the kids. There has to be a clear ownership from the registered owners to you.
The only thing you can do is to take photos and send pictures to someone else in good standing in ADGA, or have another member out, to look at your goats and have them recorded as recorded grade. Then breed them to a purebred buck...you can't use the buck you have unless he is a ADGA registered buck.
This is where in goats saying your goats are purebred without paperwork in hand is simply unethical. Selling kids out of purebred stock, isn't true unless the paperwork is in hand.
If you have any old paperwork at all, on the original bucks and does I can help you register it all...it does cost alot because your have to keep registering in generations, sending it in, waiting for the new numbers of the kids to come in, then sending it in again, plus paying late fees for the animals being over a certain age, but it can be done.
A gal purchased 2 bucklings and 3 doelings from me morethan 10 years ago. She had all the breedings and dates and kidding dates written down. We were able over the course of a month send in all the paperwork until finally her kids from last year were in her name and registered. But we first had to put into her name the 5 kid she bought from me so long ago, 3 of which were dead

If you have anything at all email me. Vicki