Note that DIY color is exactly the same as the ‘professional’ dyes, whether you buy 'em yourself at a beauty store or pay far too much for a colorist to do it. Hair dyes are simply not all that chemically complicated. So when you pay someone to color your hair, you’re paying for their expertise, and nothing else. If you know of a colorist who is competent, and you can afford it, then go for it. But I’ve heard as many horror stories about bad colorists as I have about bad home-jobs. Don’t just go and find any random salon if you go that route.
Trying a semi-perm is probably worthwhile. Again, choose a nice ashy brown. Semi-perms shouldn’t do any significant lasting damage to your hair, and since you’re going darker, and your hair is already porous from previous dyeings, it should stick ok for a few weeks at least.
However, if a permanent color didn’t stick at all, you may have actually damaged the hair strands enough that they simply can’t grab color. I’ve never witnessed this myself, but I’ve heard that it can happen. There are products that claim to help (I think one is called ‘Porofill’) and you can probably buy them at the beauty store. But I wouldn’t expect amazing results.
If Herbal Essences is a permanent color (I don’t know off the top of my head) then it does contain ‘bleach’ - all permanent colors contain enough bleaches to lift the existing color a level or two and allow the new color to ‘take’ - an oxidizer (like peroxide) is necessary to make the aniline dyes develop. So permanent colors always take some color out, and always damage your hair.
Waiting four weeks is voodoo. The hair shaft doesn’t “heal” and there’s no way for the damage to go away (no matter what conditioners may claim on the bottle) because it’s dead tissue. The half inch or so of new hair you have in four weeks will be undamaged, and your scalp, which also takes a beating in these processes, will have healed, but it won’t do anything to fix the hair that’s already there.
The safest approach is to find a semi-perm color, in an ash brown, and try that, but no guarantees that it will be incredibly effective. Semi-perms don’t last as long or produce the same vibrant results that permanent colors can. Of course, you’re probably not after vibrancy, since that’s the main problem with your hair at present. It’s probably worth a try, though, and if it doesn’t work, another attempt at permanent coloring is about the only thing left to try.
Oh, and please PLEASE don’t bleach your hair. Someone above suggested it, but colored hair is hard to bleach as it is, and it’ll damage your hair to hell. If your hair has been repeatedly colored already, bleach is gonna make it fragile and unpleasant, and it could even cause it to break near the root. I’ve heard horror stories about bleaching one time to many, leaving the person almost bald.
At any rate, I’ve always had good luck with the Clairol Professional line (you can buy it at Sally Beauty) and reasonably good results with the L’Oreal professional line (I forget what it’s called.) Good luck!