Hi @GusCE6 and @Keef . I probably shouldn't butt in (Keef knows a lot more than I do), but I am a bit paranoid about laptop batteries, partially because I don't have much knowledge, and have been caught out with something like this in the past.
First off, I realise that you don't have a hard drive, but if you have anything that you want to keep from the live environment, that is not already saved elsewhere, I would back it up.
Are you running Slacko32-6.3.0 or Slacko64-6.3.0?
I have tried to check things using Slacko32-6.3.2 on a laptop I have (I didn't have a Slacko 6.3.0 on the USB drive that I used).
If you left click on the battery icon, a text box should appear that will have battery info. Note that this will be as the system detects things, using info from the battery (I think). Particularly check the indicated charging state, design capacity, design capacity low, last full capacity and remaining capacity.
Close the text box, and maybe try going to the menu, select Leave, and then select Restart the Graphical Server. I don't know if it will do much with respect to this, but it might refresh things. Then have another look at the battery info, as above.
I guess you could also try shutting down, whilst leaving power connected, waiting a little, and then rebooting, to see if that refreshes things.
If you then intend to use Keef's approach, have everything ready to connect and turn on quickly. In the past I have had hardware battery indicators show a very low battery as full after a short period of charging, as the capacity had dropped. This is particularly likely in the situation you describe. If it is the case that the battery has lost most of it's capacity, you will not have long before the laptop will just shut down (or just drops down with no power).
With respect to the aside regarding booting other Pups from USB, there are a number of options (including one from Fatdog64). It could possibly be best to check the forum, and then make a separate post for that.
Thanks.