serious issues, please help

So I just got my moms inspiron 1440 yesterday and I started setting it up today. Its got 2gb of ram and a 250gb hardrive; windows 7 premium 64bit.

I started it up, set up passwords and what not, added some programs my mom wanted like itunes and yahoo messsenger. Now during this time I got a warning saying that the memory was about to run out. I sit there with my confused face and run the task manager. It was using about %75 of physical memory. Nothing was running except for internet explorer and yahoo messenger. The laptop freezes up completley so I shut it down and now it wont even turn on.
The power light lights up but absolutley nothing happens. Keep in mind this is a brand new laptop.

Please help Im not exactly tech savy and I cant think of anything to do.

Edit: okay got windows to run now, took out and re-inserted the ram.
but now its using %50 of memory and cpu while its just sitting. ant ideas?

 

Another question not really relating to the problem, but is it okay to leave a laptop connected to the AC adapter while the battery is in it fully charged?

 

With 2GB RAM, you should really be running a 32-bit OS. Only with 4GB RAM should 64-bit be considered. This would explain the excessive memory usage.

Is this a new system? You should reinstall Windows. That will get rid of bloatware and probably will speed the system up.