I have a similar or same issue with Ubuntu 14.04.01 on a desktop with a Ethernet connection only that worked with Ubuntu 8.04 since 2006. Since updating, no internet.

I decided to upgrade and did a clean install of Ubuntu 14.04.01 trusty and I NEVER had Internet again on this dektop. I am sure (tested) that the cable is OK, the hardware is OK, the internet connection is OK 

I have tried a lot of things and a long time spent with excellent support form the comunity in Italy via IRC did not solve the issue.

uname 
Linux marco-desktop 3.13.0-32-generic #57-Ubuntu SMP Tue Jul 15 03:51:08 UTC 2014 x86_64 x86_64 x86_64 GNU/Linux

dmesg|grep tg3
[    1.156680] tg3.c:v3.134 (Sep 16, 2013)
[    1.230990] tg3 0000:03:00.0 eth0: Tigon3 [partno(BCM95789) rev 4101] (PCI Express) MAC address 00:0f:ea:4c:4e:1a
[    1.231000] tg3 0000:03:00.0 eth0: attached PHY is 5750 (10/100/1000Base-T Ethernet) (WireSpeed[1], EEE[0])
[    1.231006] tg3 0000:03:00.0 eth0: RXcsums[1] LinkChgREG[0] MIirq[0] ASF[0] TSOcap[1]
[    1.231012] tg3 0000:03:00.0 eth0: dma_rwctrl[76180000] dma_mask[64-bit]

ifconfig eth0
eth0      Link encap:Ethernet  HWaddr 00:0f:ea:4c:4e:1a  
          UP BROADCAST MULTICAST  MTU:1500  Metric:1
          RX packets:0 errors:0 dropped:0 overruns:0 frame:0
          TX packets:0 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000 
          RX bytes:0 (0.0 B)  TX bytes:0 (0.0 B)
          Interrupt:18 

interfaces
# interfaces(5) file used by ifup(8) and ifdown(8)
auto lo
iface lo inet loopback

lshw -C network
  *-network
       description: Ethernet interface
       product: NetLink BCM5789 Gigabit Ethernet PCI Express
       vendor: Broadcom Corporation
       physical id: 0
       bus info: pci@0000:03:00.0
       logical name: eth0
       version: 11
       serial: 00:0f:ea:4c:4e:1a
       capacity: 1Gbit/s
       width: 64 bits
       clock: 33MHz
       capabilities: pm vpd msi pciexpress bus_master cap_list ethernet physical tp 10bt 10bt-fd 100bt 100bt-fd 1000bt 1000bt-fd autonegotiation
       configuration: autonegotiation=on broadcast=yes driver=tg3 driverversion=3.134 firmware=5789-v3.29a latency=0 link=no multicast=yes port=twisted pair
       resources: irq:18 memory:e4000000-e400ffff

lspci -nnk
00:00.0 Host bridge [0600]: Intel Corporation 82945G/GZ/P/PL Memory Controller Hub [8086:2770] (rev 02)
	Subsystem: Gigabyte Technology Co., Ltd Device [1458:5000]
00:01.0 PCI bridge [0604]: Intel Corporation 82945G/GZ/P/PL PCI Express Root Port [8086:2771] (rev 02)
	Kernel driver in use: pcieport
00:1b.0 Audio device [0403]: Intel Corporation NM10/ICH7 Family High Definition Audio Controller [8086:27d8] (rev 01)
	Subsystem: Gigabyte Technology Co., Ltd GA-8I945PG-RH Mainboard [1458:a102]
	Kernel driver in use: snd_hda_intel
00:1c.0 PCI bridge [0604]: Intel Corporation NM10/ICH7 Family PCI Express Port 1 [8086:27d0] (rev 01)
	Kernel driver in use: pcieport
00:1c.2 PCI bridge [0604]: Intel Corporation NM10/ICH7 Family PCI Express Port 3 [8086:27d4] (rev 01)
	Kernel driver in use: pcieport
00:1d.0 USB controller [0c03]: Intel Corporation NM10/ICH7 Family USB UHCI Controller #1 [8086:27c8] (rev 01)
	Subsystem: Gigabyte Technology Co., Ltd GA-D525TUD [1458:5004]
	Kernel driver in use: uhci_hcd
00:1d.1 USB controller [0c03]: Intel Corporation NM10/ICH7 Family USB UHCI Controller #2 [8086:27c9] (rev 01)
	Subsystem: Gigabyte Technology Co., Ltd GA-D525TUD [1458:5004]
	Kernel driver in use: uhci_hcd
00:1d.2 USB controller [0c03]: Intel Corporation NM10/ICH7 Family USB UHCI Controller #3 [8086:27ca] (rev 01)
	Subsystem: Gigabyte Technology Co., Ltd GA-D525TUD [1458:5004]
	Kernel driver in use: uhci_hcd
00:1d.3 USB controller [0c03]: Intel Corporation NM10/ICH7 Family USB UHCI Controller #4 [8086:27cb] (rev 01)
	Subsystem: Gigabyte Technology Co., Ltd GA-D525TUD [1458:5004]
	Kernel driver in use: uhci_hcd
00:1d.7 USB controller [0c03]: Intel Corporation NM10/ICH7 Family USB2 EHCI Controller [8086:27cc] (rev 01)
	Subsystem: Gigabyte Technology Co., Ltd GA-D525TUD [1458:5006]
	Kernel driver in use: ehci-pci
00:1e.0 PCI bridge [0604]: Intel Corporation 82801 PCI Bridge [8086:244e] (rev e1)
00:1f.0 ISA bridge [0601]: Intel Corporation 82801GB/GR (ICH7 Family) LPC Interface Bridge [8086:27b8] (rev 01)
	Subsystem: Gigabyte Technology Co., Ltd Device [1458:5001]
	Kernel driver in use: lpc_ich
00:1f.2 IDE interface [0101]: Intel Corporation NM10/ICH7 Family SATA Controller [IDE mode] [8086:27c0] (rev 01)
	Subsystem: Gigabyte Technology Co., Ltd Device [1458:b002]
	Kernel driver in use: ata_piix
00:1f.3 SMBus [0c05]: Intel Corporation NM10/ICH7 Family SMBus Controller [8086:27da] (rev 01)
	Subsystem: Gigabyte Technology Co., Ltd GA-8I945PG-RH/GA-D525TUD Mainboard [1458:5001]
01:00.0 VGA compatible controller [0300]: NVIDIA Corporation NV44 [GeForce 6200 TurboCache] [10de:0161] (rev a1)
	Subsystem: XFX Pine Group Inc. Device [1682:2146]
	Kernel driver in use: nouveau
03:00.0 Ethernet controller [0200]: Broadcom Corporation NetLink BCM5789 Gigabit Ethernet PCI Express [14e4:169d] (rev 11)
	Subsystem: Gigabyte Technology Co., Ltd Device [1458:e000]
	Kernel driver in use: tg3
04:00.0 Multimedia audio controller [0401]: Creative Labs CA0106 Soundblaster [1102:0007]
	Subsystem: Creative Labs SB0570 [SB Audigy SE] [1102:100a]
	Kernel driver in use: snd_ca0106
04:06.0 RAID bus controller [0104]: Integrated Technology Express, Inc. IT8212 Dual channel ATA RAID controller [1283:8212] (rev 13)
	Subsystem: Integrated Technology Express, Inc. IT/ITE8212 Dual channel ATA RAID controller [1283:0001]
	Kernel driver in use: pata_it821x

There was no trace of trying to connect 

I have tried manually starting the eth0 with

sudo dhclient eth0

no connection was possible

I had this long list of DHCPDISCOVER on eth0 to 255.255.255.255 port 67 as described above

I did delete the dhclient.leases file as suggested above, doing
rm /var/lib/dhcp/dhclient.*

this did not solve the issue.

Neither I neither geeks on the IRC channel managed to solve this yet.

I am fairly upset as you can imagine.

thanks