The inability to connect the Kindle Fire to Wi-Fi is particularly ugly given that the tablet has no 3G service; the majority of its content -- streaming video, music, apps, and more -- is hosted in the cloud; and the 8GB of internal storage (only 6.54GB of which is user-accessible) isn't large enough to do much more than read e-books.
But if your Kindle Fire is stuck on the "acquiring IP address" screen and refuses to load, perhaps some of these found fixes will help.
Update Your Kindle Fire Software: Amazon recently released version 6.2 of its Kindle Fire software -- the same update that removed root access. Though version 6.2 does not specifically mention bug fixes for Wi-Fi problems, many users on Amazon's support forums found that updating from 6.1 helped the device talk to routers.
Reset to Factory Settings: Sometimes devices need to have a fresh start. Go to the gear icon (settings), then More, then Device, then Reset. This helped some users reconnect to the Internet.
Tinker with the Router: Resetting your router helped some, whereas others had to change to a static IP instead of using a DHCP address (check your router's manual). This is done by turning off Wi-Fi on the Kindle Fire, deleting all DHCP records on the router, and then resetting the router.
Get a New Router: Sometimes the routers supplied by cable companies aren't up to snuff and need to be replaced by newer models in order to improve wireless connections. It's worth a quick call, online chat, or email to see.
Give it Time: A large number of forum posters found that by giving it a rest, the Kindle Fire somehow found its way back to normalcy and started to work -- with no known tinkering other than powering down the Kindle Fire and, in some cases, the computer used to side-load the device.
Call Amazon Support: Amazon's support service is one of the industry's best, and although many customer service reps have acknowledged the Kindle Fire's Wi-Fi issue as "recurring" and "known," there has yet to be an Amazon-sanctioned fix -- yet.