Alienware? Too costly. Unless you're looking at the M11x. Which is 11", and has a nice price. Other than that, their laptops are really expensive. Not to mention they're owned by Dell now. =/
Toshiba is fairly good. You'd have to do some research before finding a gaming spec'd laptop made by them though. I suggest looking at ASUS or Acer. They have some decent gaming laptops at a good price.
Gaming laptops have 2-3 hours of battery life though. And most come with 320GB or 500GB hard drives now. Memory? Most laptops come with 2GB ram. I've seen Dells with 6GB ram, but at a $1299 price.
Up to you, though.
And honestly, fast broadband speeds really depend on your internet provider. Most NIC's are fast speed standard now. Although my old laptop did come with a modem built in...
Lenovo does have some gaming specs laptop though they are still more well known for their durability and office-use specs.
Alienware, have to agree with you, they are hella expensive and simply not worth the money
Toshiba I recommend looking for the high end satellite series, they are available in quite good specs and good price too (I saw one with i5 and 500 Gb Hard disk, Built in wireless modem, 4Gb RAM at under 1200 AUD which is quite a bargain) or Qosmio Series if you're looking for stylish look (I love that series' Red lining, dang they look beastly)
Battery-wise, Cloud pretty much said it all.