If you want to game on a laptop, it will cost you $2,000+ and it will EAT batteries die to the graphics card.
You can build a seriously fast gaming PC for $800 through newgg.com.
$76 - Penitum e2140 (uses the Core 2 chip design)
$40 - 120mm heatsink / fan for the CPU, lets you overclock from the stock 1.6ghz to 2.8ghz+
$130 - Gigabyte P35 motherboard (upgradeable to Quad core)
$75 - 2gb DDR2-800 RAM
$250 - Nvidia 8800GTS 320mb video card
$44 - Cooler Master Centurion case
$80 - 320gb Seagate SATA hard disk
$85 - 500watt+ FSP, OCZ, Hyper, etc. level power supply
$30 - DVD burner
The above will play any game at MAX settings.
It's very easy to put a PC together, I mean do you really think the people on the assembly lines at Dell/HP warehouses are skilled?
There are plenty of instructional videos on youtube.com and great help forums at anandtech.com and tomshardware.com.
OR
Laptop prices have became quite reasonable over the last year, and catching a good sale will make it downright cheap.
Looking through the Sunday ads, this is easily the best for the money at $449 (after rebate)
http://www.circuitcity.com/ssm/Compaq-Presario-15-4-Widescreen-Notebook-PC-F572US/sem/rpsm/oid/185304/catOid/-12963/rpem/ccd/productDetail.do
It has:
AMD Dual-core CPU (2 processors in one)
1gb of RAM
DVD / CD burner
80gb hard drive
wireless internet
This one from Office Depot is also a steal at $479 after rebate, with all the same features, just using an Intel CPU instead of the AMD:
http://www.officedepot.com/ddSKU.do?level=SK&id=630065&Ntt=a135-s4666&uniqueSearchFlag=true&An=text
Honestly, spending $7,8, or even $900 simply gets you a 120gb hard drive 2gb of RAM (with a SLIGHTLY faster clocked CPU).
And as you can see:
http://www.youtube.com/results?search_query=laptop+RAM+install&search=Search
http://www.newegg.com/Product/Product.aspx?Item=N82E16820208300
Upping the 1gb of RAM to 2gb is only $38.
And 80gb's of hard drive space is enough for pretty much everything someone would do on a laptop. Now if she's a movie pirate or something, she might want some more space lol.
If you have any questions let me know.