From one flashoholic to another, how ya doing brotherI am a cheap flashlight junkie and have purchased more than a dozen of those 3-4 dollar Cree single AA flashlights from China. Given a lot away also. Drives me nuts when those push button switches on the back fail to work. In fact I was looking for a cure to that just a day ago.
Sounds like your talking about the Sipik and/or the SK68. Those are the ones that can take either a single AA or a 14500 lithium ion battery. With the AA you'll get about 80ish lumens, which is quite bright. With a 14500 you'll pump that up to around 300 lumens which is great for such a small light (though these days you can get something like a Nitecore EA11 or EC11 that pumps out 900+ on turbo). If you haven't been there, take a look at budgetlightforums and you'll see all kinds of mods and repairs for various lights. You can easily repair the switches. Here is an example, it's a typical 18650 light and not a Sipik or SK68 but it's probably similar. The tail cap part starts around the 1:10 mark.
Budgetlightforums would probably have info on parts and where to get them