Computer Problem. Can you help?

Here’s the problem….or problems:

1) When I plug my charger into my computer, it does not stay in right. It’s not necessarily loose, but the connection or something seems to be iffy. If I move my computer the littlest bit, the charger will become “unplugged”. Basically, if I’m not careful, I could sit there thinking my computer is charging, but the blue light (where you plug it in) isn’t on so the computer is dying instead. Hopefully that makes sense. :o P
2) This could be tied to the first problem, but my battery pretty much sucks. I have to have my computer plugged in all the time or else it dies within like 5 minutes. And even then it doesn’t get all the way to 0% before it completely shuts down. Sometimes it’s at 30% and *bam* shuts off. Keeping my computer plugged in all the time though can prove to be a pain though, as you can see from #1.
3) My computer keeps telling me I need to install updates. A little box is constantly popping up in the corner saying that basically in 15 minutes my computer is going to restart to finish updating. It gives me the option to postpone if I want. However, even if you let it restart, it acts like it’s updating but then it says “updates not configured correctly, reverting to…. etc.” So, really, it doesn’t seem to me like it’s updating at all and I can’t figure out how to fix it.

I have an HP, Windows Vista, Laptop.

Not sure if any of those problems sound familiar or even make sense. If you need more info, just tell me! I’m hoping to just get some insight as to whether it sounds like (with the cord/battery deal) it’s worth getting fixed or if I should just buy a new computer.

Thanks in advance-

Computer Problem. Can you help?