I have to jiggle and push the AC plug in quite often on my Gateway laptop.
It doesn't seem to fit very tight at all.
You might check to see if yours is coming loose sometimes,
the screen should get brighter right away if that connection is the problem.

Ours was a refurbished one and at the time we bought it there had been a big recall on lots of laptop batteries. So we did get a brand new one of those.

If you go to the Dell website you should be able to look up the laptop & maybe there is battery info/details, recalls, tips, FAQs.

If nothing else maybe email them telling them your problems , they might send you a new one or a discount coupon for a new battery.


wireless-
What program is telling you about the unsecured wireless?
your anti virus or something on the windows part of it?
I don't know if you have an internet security suite program {covers wireless & network security also} or anti virus & antispyware & firewall...

depending on your set up maybe you can rescan or check settings to see what might have changed? If it was secure before??

If all else fails I suppose you could do a system restore back to a day when it was secure if not too long ago..

I would just be sure it is a program you have installed or on your windows system that is giving you the notice and not some odd ball hijacking program or site.

If you aren't sure about the wireless settings - you might need someone with a little experience to check your settings in person.

Hopefully someone else is really up on this stuff and might have more input.
I just am self taught and learned by poking around on my systems but I don't know enough on all systems or how to to explain it all.