I would suspect that some batteries have reverse polarity, so they do not work with "Off-brands", or so they only work with "Off-brands". That could have been part of the OEM deal. (They would do that, so the other dealers of batteries look like they are selling junk, and you keep buying supplies from the company who sold you the battery. It is called "brand-locking". EG, like I-Pod... anyone can make an adaptor but I-Pod would sue them for selling it, if they did not pay for the rights to use it. However, if you reversed two wires, so it does not work on an I-Pod, but it works on your J-Pod brand... I-Pod can't do anything. NOTE: I-Pod will not let you manufacture a low-quality compatible device, and allow you to sell it for more than they offer.)
However, I suspect that there are two things going on here...
The battery with the light lit-up, but no action, seems to have a faulty vaporizer contact on the battery side. EG, the light is turned-on by the internal switch but no power passes through the switch, to the inner terminal connection. (A simple volt-meter would confirm that issue. Perhaps the contact had some varnish or solder-rosin or just manufacturing plastic/wax on the contact. (Tapping the battery might scrape the thin layer of undesired material, exposing a better contact area. If the contact area was too small, it would be carbon from electrical gap arking.)
If the light does not light, or stays on... More than likely, it is the contact switch jammed open or closed. Could be some manufacturing debris that fell inside, and has finally slipped into a location where it should not be. Could also be poor production parts, which are over-sized or under-sized, and too tight to move freely. Rarely, but still possible, the battery wrapping could have loosened and worked into a place which breaks the electrical connection, or it has leaked inside, corroding the contacts.
If there is truly a circuit controller, as I know some do have, and others do not. There is a chance that the battery was allowed to over-charge, or was allowed to run below-charge. This would cause excessive voltage or excessive amperage through the micro-chip, which would cause the thin gold wires or thin-silicon-wafer to fry. (You can usually smell when that happens, as the microchip case heats-up like the coil, and melts with a funny electrical odor.)
The battery chargers used for these devices are just raw power. The regulator is inside the battery compartment, and all except the V7-V9 DSE 901 and all new models, the regulator is dumb. It switches to low-power or "top-off" charge when done charging. The older models should be immediately removed once charged completely. Leaving them on the charger will over-charge the battery. (Just like a cell-phone from the old days. you know, five years ago.)
The new V7-V9 DSE 901 models have the true "Off" charger state, once completely charged. EG, they use an energy-star mode, of sorts. They shunt off to a mini-load, as opposed to trying to trickle charge the battery infinitely when it is full. (The old microchip is also known as the laptop exploding battery charger chip.)
It is better to charge the battery before it goes dead. If you run it down to dead, and recharge it every time, you will kill it within a year, or after 150 charges. If you switch batteries between use, and charge both before they have run-down, you will get over 600 charges, or the full, "300 complete charges".
Some of this is computer knowledge, some is RC car knowledge, some is cell-phone knowledge, some is robotics knowledge, most is trial and error. (Everyone has a "Special" way... few actually work because of that "Special way", while the rest would have worked no matter what, or just don't work at all.)
In any event, if the battery you have is the one provided with the model, or provided by the person who sold you that same model, (Thus being a compatible battery.) You have every right to demand a replacement until you get a functioning replacement. Or you are entitled to a full refund, as USA law dictates. It is an agreement when selling any item in the USA for USA currency, that the item you sell, works as described. The only exception is the term, "Sold as is". (No refunds only applies for the return of a working device, not for the return of a device sold as working, which does not actually work, or has failed within a reasonable time period.)
If they fail to comply, go to the BBB or call your local news station, or setup a petition with all the gathered proof you can. A class action lawsuit, or even a personal call from your lawyer will set them in the right path. (Usually they just run and hide after that, and go out of business for buying from third-parties who don't support the seller, making the seller look bad, by selling them junk-devices. Remember, in China, they have multiple runs... Pre-production, where 50% work, followed by a grey area where 80% work, followed by production where 92% work. They don't throw away all those assembled pre-production runs... they sell them cheaper, without labels or relabeled. They don't strip them down, and reassemble them correctly. That takes too much time, and they can sell them for more than it costs to rework the defunct parts.)
They also allow OEM design. OEM buyers can request cheaper parts, more expensive parts, better quality control, additional testing, pre-charged batteries, logo branding, and alternative package designs. OEM which are demo-models are usually the best, as they are the showcase devices which the OEM buyers use to determine what extra features they want added, or cut back-on. (Look at the Chinese scooter market. Five companies make almost all of the 800 branded scooters you see, all with interchangeable parts, though some parts are better or worse, and all usually work. Same here, with all the subtle changes in filters, screw threads, paint-jobs, battery quality, charger styles, etc...)
NOTE: Most of that was observation from existing dealings with manufactures. I also worked for a plastic manufacture of parts, and we did a lot of that here in America also. However, we never sold another persons junk, we ground it up, or gave it to them. They sold it or gave it away, or used it for further processing or as demo-items or dead displays.