Not being a douche here, but unless you have worked with laptops for sometime, don't count on one little thing like that to choose what kind of laptop you get. They really didn't do much explaining on how the data was gathered and what kind of malfunctions happened. I have a problem with charts like that because you don't know about their data collection methods. HP is one of the leader in laptops, while ASUS goes under the radar often. I wonder if this is why HP (selling "more") has "more" malfunctions while ASUS (selling "less") has the "least" malfunctions. I don't know, but it just makes me wonder.
At any rate, I'm free now, so I'll take a look at some laptops for you in just a bit.
LENOVO IdeaPad Y550 - $739 + tax (shipping free?) Trade off is the 5400RPM drive
Intel Core 2 Duo processor T6600 (2.20GHz 800MHz 2MBL2)
Genuine Windows 7 Home Premium 64 Bit
nVidia Geforce G 210M graphic card with 512MB memory
15.6 HD WLED Glossy, 1366*768 with 1.3M integrated Camera
3 GB PC3-8500 DDR3 SDRAM 1066MHz SODIMM Memory (2 Dimms)
250GB Hard Disk Drive, 5400rpm
SuperMulti DVD Recordable (Tray type)
Broadcom Integrated Gigabit Ethernet (802.11G)
6 Cell Lithium-Ion 2.6Ah
Grey Keyboard
HP dv6t series - $799 (+ tax; shipping?) Trade off is price
Color Espresso Black
Operating system Genuine Windows 7 Home Premium 64-bit
ntel(R) Core(TM)2 Duo Processor T6600 (2.2GHz, 2MB L2 Cache, 800MHz FSB)
FREE Upgrade to 3GB DDR3 System Memory (2 Dimm) from 2GB DDR3 System Memory (2 Dimm)
FREE Upgrade to 500GB 7200RPM SATA Hard Drive from 250GB 7200RPM SATA Hard Drive
512MB ATI Radeon(TM) HD 4530 Graphics
15.6" diagonal High Definition LED HP Brightview Widescreen Display (1366x768)
LightScribe SuperMulti 8X DVD+/-RW with Double Layer Support
Webcam
Wireless-G Card
HP Color Matching Keyboard
6 Cell Lithium Ion Battery
Microsoft(R) Works 9.0
HP dv6z series - $705 Trade off is CPU and RAM
Espresso Black
Operating system Genuine Windows 7 Home Premium 64-bit
AMD Turion(TM) II Dual-Core Processor M540 (2.4GHz, 1MB L2 Cache)
FREE Upgrade to 3GB DDR2 System Memory (2 Dimm) from 2GB
DDR2 System Memory (2 Dimm)
250GB 7200RPM SATA Hard Drive with HP ProtectSmart Hard Drive Protection
50% OFF! 512MB ATI Mobility Radeon(TM) HD 4530
15.6" diagonal High Definition LED HP Brightview Widescreen Display (1366x768)
SuperMulti 8X DVD+/-R/RW with Double Layer Support
Webcam
Wireless 802.11b/g/n Card
6 Cell Lithium Ion Battery
Microsoft(R) Works 9.0
There you go. If it was me and I had to stick with that $700 budget, I'd go with the first one. I'd stay away from the last one if you can. I wouldn't get an ACER...personal choice. ASUS isn't too bad.
EDIT:
Here's a decent one on the Egg.