If you do not mind buying an open box laptop with only a 60 day warranty (but the seller offers an option to buy an extended warranty), then perhaps the 15.6" Dell Latitude 3540 might be of interest for $609.
http
/www.ebay.com/itm/Dell-Latitude-3540-New-Win-8-Laptop-i5-4200U-4GB-500GB-Webcam-DVDRW-15-6-FHD-/291199124488?pt=Laptops_Nov05&hash=item43ccd20408
Core i5-4200u
Radeon HD 8850 (Venus Pro)
1920x1080 resolution screen
4GB of RAM
No backlit keyboard
I have this laptop which I bought refurbished from eBay with a 1 year warranty earlier this year from a different sell at an even lower price. I like the laptop a lot. Despite only having a standard hard drive Windows 8 load to the login screen in about 5 seconds. Not sure how since it does not even have a SSD cache. I also like the fact that it has a matte anti-glare screen. I really do not like glossy screen because they are very reflective.
The Radeon HD 8850 / Venus Pro dedicated GPU's overall performance is very close to the nVidia GTX 755m and GTX 660m. See following for benchmarks. It performs the same as the GTX 650m in Skyrim though.
http
/www.notebookcheck.net/AMD-Radeon-HD-8850M.87118.0.html
I bought the laptop because of the 1920x1080 resolution for use other than games. However, you will likely have to run games at lower resolution to get better performance. Dedicated laptop graphic chips are no where near the performance of their desktop counterparts.The Radeon HD 8850m is slower than a desktop Radeon HD 7770.
I cannot say how well Skyrim performs because I stopped playing that game before I bought the Dell Latitude 3540. The only game I am currently play is Star Trek Online.
Speakers are not the greatest because this is a business laptop, but they are okay. You can always connect external speakers if you want. The only thing really lacking though is it does not have a backlit keyboard.