Gumby, I struggled with this same problem about a month ago ('98 V70). All of your symptoms. I swapped the battery twice in MY remote, to no avail. However, HER remote worked without fail. Finally, I hotfooted it to Radio Shack, picked up a fresh battery there, and since then, no problems. Two points to ponder: if all locks respond to the key, but not to the remote, it's still the same vehicle battery supplying the solenoids which operate the locks. Second point - not all "new" batteries are equal. I was reading an article about the service life of batteries in digital calipers, and was not too surprised to learn that the original issue batteries in an instrument manufactured in China (for example) frequently offered a significantly shorter shelf-and-service life, not to mention dodgy voltage levels, than a fresh brand name article. This info could have saved me considerable frustration whilst solving my own problem. BTW, the batteries I was using to try to bring my remote to life had been purchased at a great price, carded, from an auto supply shop during one of their sales - perhaps not so great a bargain after all.
Cheers, Garth.