There is no way around it. You are being instructed to restore the iPad using iTunes. You have to do this with a computer. It does not have to be your computer. Any computer running the latest version of iTunes will do, but it will totally erase your iPad.
If your laptop is not working, I assume that you have been backing up with iCloud. After you restore the iPad, you can restore from the iCloud backup and will be OK. If you don't back up, you will have to start all over again and download all of your purchased content again in the iStores. Much of that paid content will be free as long as you use the same Apple ID and as long as the content is still available in the iStores.
Most likely, you will need to use recovery mode in order to restore, and you can read about it here.
I honestly think that this was just a fluke occurrence. This could happen to anybody, and I don't think that it is necessarily related to the iPad running out of battery power - if that is what you are asking about.
I have let my iPad battery run down until it shut off by itself on a few occasions when I wanted to run the iPad through a charge cycle to calibrate the battery gauge. I was right there though each time that the battery ran down and the iPad shut off, so that I could plug it in and start the recharge process.
I mean it's unlikely I'll keep the ipad always charged.
I'm not sure what you mean by this, but your iPad does have to have battery power in order to use it. I hope that you aren't saying that you are going to make a practice of letting the battery run down completely. I'm probably misinterpreting what you mean.... I hope.
You can plug your iPad's USB cable into a laptop's USB port and the iPad will charge, but slowly (even though you might get a notice that it's not charging.
Apple recommends that once a month you let the iPad fully discharge & then recharge to 100%.
How to Calibrate Your Mac, iPhone, or iPad Battery