About 10-11 years ago, both bathroom sinks quit draining. After many attempts with snakes and chemicals we finally just stopped using the bathroom sinks because we knew by then the pipes in the wall would need to be replaced and we couldn't afford to hire anyone. We are on limited income. All other drains in our home work fine. Now, we are wanting to get this done. We are old now. Will this be difficult to be done?

Do the other drains in that bathroom (tub, shower, toilet) work ok? If they do then the problem could be a clog in the sink drain common pipe, a competent drain cleaning service should be able to clean it out without replacing any pipes. Get someone in there to evaluate and attempt to clean it.

If the sinks are on the same wall they likely share a common drain, the clog is probably at the base of the stack where the drain turns from vertical to horizontal. A competent plumber could likely resolve the issue without much difficulty.

If not a blockage, what other avenue could you look at?