cant paint over a wallpaper border?

From what you have already tried you could have take the border down just as quick. Use a wall paper scoring tool (from lowe's) and "score" the border. Fill a spray bottle with fabric softener (the cheaper the better it works) and spray the border. Let it sit for a few minutes and the border will peel right off the wall. Cheap, fast, easy and it really works - I was actually amazed at how much better it works than the expencisve wall paper remover stuff they sell at Lowe's.

If the paper went up it must come down, there is no such a think that you can't and cannot do , it takes more time that's all ! with a blade lift a piece of the border and peel off the top layer of the paper border, then spray warm water to soften the base coat and the glue, scrape off the residue and wash the walls down with TSP , and either paint or re-wallpaper . But don't paint over the paper, because you will see the line of the border and this wont give you a smooth surface.

Strip the wallpaper they sell products that help it come off easy

Or you might want to get a primer like kilz and try that then paint over the primer

Definitely need to use Diff or another product to strip wallpaper first.