This question already has an answer here:
In late February 2013 I installed the latest updates on my Ubuntu 12.04 system (an Asus Eee 1215T), rebooted, and after that it was no longer able to make a network connection over wi-fi. It just repeatedly asks me for the WPA password. I enter it, but the connection is not made and it asks for the password again. I have made no changes to the wi-fi router for at least 6 months, and other wi-fi devices I have still connect without trouble. The only thing that changed was the Ubuntu update.
Update: After some digging, I have found the problem and a solution. Close reading of /var/log/syslog revealed that the computer was connecting to the wi-fi router without trouble, but it was failing the DHCP negotiation. Read my answer below for details, as soon as this question gets reopened. :) I'm leaving my old information in the question for reference, in case anyone finds it relevant.
BTW, for those that marked my question as a duplicate, I think it isn't. While the solution in the purported duplicate question's answers might have worked (I didn't try it), mine was a new problem introduced by a January 2013 Ubuntu update, and not the classic Broadcom problem reported in 2012, and it was solved with a different method.
dmsg shows the device as a BCM4727:
$ dmesg | grep -i bcm [ 20.632433] eth1: Broadcom BCM4727 802.11 Hybrid Wireless Controller 188.8.131.52 (r326264)
lshw shows it as a BMC4313:
$ sudo lshw -C network PCI (sysfs) *-network description: Wireless interface product: BCM4313 802.11b/g/n Wireless LAN Controller vendor: Broadcom Corporation physical id: 0 bus info: pci@0000:02:00.0 logical name: eth1 version: 01 serial: 48:5d:60:6d:d8:59 width: 64 bits clock: 33MHz capabilities: pm msi pciexpress bus_master cap_list ethernet physical wireless configuration: broadcast=yes driver=wl0 driverversion=184.108.40.206 (r326264) latency=0 multicast=yes wireless=IEEE 802.11abg resources: irq:16 memory:fbefc000-fbefffff
The specifications page does not make the wi-fi chipset clear, unfortunately.
In case it is relevant, here is
$ lsmod | grep wl wl 2906597 0 cfg80211 178877 1 wl lib80211 14040 2 lib80211_crypt_tkip,wl
I tried removing and reinstalling the Broadcom STA wireless driver through System Settings --> Additional Drivers, but that didn't help, even after a reboot.
The page WiFi problem after Ubuntu 12.10 update has some promising suggestions in its accepted answer, but seems to be specific to 12.10 and the BCM4312, not my (possibly) BCM4313. Any suggestions?