I'm not entirely sure what you mean by "power brick", but if it means something listed by another name below, then skip any suggestion you replace this item since you appear to have confirmed it works using a different computer - but still do the various recommended tests involving it so we can rule out other possible causes (and to double-check things on the problem laptop).
Remove the battery, gently clean the leads with a tissue, and replace the battery securely and see if that makes any difference.
Of course, if you have another battery (a backup or one in another computer that is the same manufacturer, make, and model), try replacing the battery and see if that makes any difference.
When you push the power button, does anything at all happen? Are there any beeps or flashes on the screen, or noises like the hard drive spinning up or the CD drive spinning up, or the power supply fan turning on, or any lights whatsoever turning on or flashing? I know you said it is not turning on at all, but I want to be sure we mean the same thing when we say that. It seems like it did something at first and then went from partial failure at first (with some lights flashing in a way you'd never seen before) and then after some fiddlng around (which we all would have tried - so don't blame yourself), it went to complete failure which is where it now stands.
Try removing the AC adapter and see if you can start the laptop from the battery alone. If so, you have a bad adapter and need to replace it. If not, we've not really learned much because we don't know how much if any charge is contained in the battery.
Try removing the battery and just using the AC adapter and see if you can start the laptop that way. If so, the problem may be either the adapter or the battery (or the cabling between them). You will need to replace one or both - but I'm not sure how to determine which is the cause (or if both are problems). Replace one and if that doesn't work, then restore the first and replace the other and if that doesn't work, then replace both and that should do the trick. If that still doesn't work, then it is likely to be the cabling or the electronics between the devices - and for that you'll need to have it serviced by a professional computer hardware repair technician.
If that doesn't work, then unless you are VERY good with computers, laptops, and electronics (and have the right equipment and testers and access to replacement parts), I would suggest it's time to take it to a competent computer repair technician for service. Do NOT use Geek Squad or any place like that - find a true professional (or return it to the manufacturer for service). It could be something as simple as a defective power button (which even if "simple" is pretty much beyond most to repair). It could be a bad power supply or something as simple as a loose connection somewhere. It could also be something much more serious. It's very hard to tell with almost no information to go on.
I am, however, almost 100% certain it is a hardware and not a software problem. At any point in this process, especially once it reaches the stage of replacing parts, if you prefer not to be buying and testing different components and simply want to resolve the problem without further bother, just stop there and take it in for servicing.
I hope this helps and that it turns out to be something simple and easy (and inexpensive) to repair.
Good luck!
