HA! I just put together a $300 desktop build for you, and THEN I realized you are asking about a laptop. Sorry! Here is my $300 desktop build anyway
PCPartPicker part list:
http://pcpartpicker.com/p/3vsxo
Price breakdown by merchant: http://pcpartpicker.com/p/3vsxo/by_merchant/
Benchmarks: http://pcpartpicker.com/p/3vsxo/benchmarks/
CPU: AMD A8-5600K 3.6GHz Quad-Core Processor ($97.74 @ Amazon)
Motherboard: ASRock FM2A75M Pro4+ Micro ATX FM2+ Motherboard ($59.99 @ Micro Center)
Memory: G.Skill Ripjaws Series 4GB (2 x 2GB) DDR3-2000 Memory ($49.99 @ Newegg)
Storage: Western Digital AV-GP 320GB 3.5" 5400RPM Internal Hard Drive ($36.89 @ Amazon)
Case: Antec One ATX Mid Tower Case ($34.99 @ NCIX US)
Power Supply: Corsair Builder 430W 80+ Bronze Certified ATX Power Supply ($19.99 @ Micro Center)
Total: $299.59
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-04-20 21:56 EDT-0400)
It would be decent for 720p gaming and maybe 900p, but it would not be very good @ 1080p