"No Internet Access" indicator, but internet access works

Question

We've got a few machines at a couple different clients that have the windows networking systray exclamation mark indicating limited network connectivity.  The supposed error is "no internet access", though the internet works fine in every
case.  It is a very visible issue generating a lot of complaints, and the clients have a tendency to associate it with all kinds of other unrelated problems.
To clarify:
Not all machines have the icon
Problem machines all have the same basic setup as non-problem machines
Some problem machines are win8, some win7
They don't share common hardware specs
I have tried several things, including:  reset ip stack, give manual ip settings to network adapter, disable ipv6, disable/re-enable adapter, all without success.
I don't know where to go to troubleshoot this.  Is there a log with this info?  Is the network connectivity check process well documented somewhere?

Answer 1

The issue occurs on ethernet and wireless.  I haven't been able to tell what the problem machines have in common.  The issue is basically permanent.  Sometimes an IP stack reset will "cure" the problem temporarily, but it returns.
Here's an ipconfig /all from one of the trouble machines:
Windows IP Configuration
   Host Name . . . . . . . . . . . . : XXXXXXX
   Primary Dns Suffix  . . . . . . . : klc.local
   Node Type . . . . . . . . . . . . : Hybrid
   IP Routing Enabled. . . . . . . . : No
   WINS Proxy Enabled. . . . . . . . : No
   DNS Suffix Search List. . . . . . : klc.local
Wireless LAN adapter Wireless Network Connection 2:
   Media State . . . . . . . . . . . : Media disconnected
   Connection-specific DNS Suffix  . : 
   Description . . . . . . . . . . . : Microsoft Virtual WiFi Miniport Adapter
   Physical Address. . . . . . . . . : 24-77-03-9E-xx-x1
   DHCP Enabled. . . . . . . . . . . : Yes
   Autoconfiguration Enabled . . . . : Yes
Wireless LAN adapter Wireless Network Connection:
   Connection-specific DNS Suffix  . : klc.local
   Description . . . . . . . . . . . : Intel(R) Centrino(R) Ultimate-N 6300 AGN
   Physical Address. . . . . . . . . : 24-77-03-9E-xx-x2
   DHCP Enabled. . . . . . . . . . . : Yes
   Autoconfiguration Enabled . . . . : Yes
   Link-local IPv6 Address . . . . . : fe80::edb8:5d03:14cc:3f8d%13(Preferred) 
   IPv4 Address. . . . . . . . . . . : 10.100.30.105(Preferred) 
   Subnet Mask . . . . . . . . . . . : 255.255.255.0
   Lease Obtained. . . . . . . . . . : Tuesday, October 07, 2014 10:35:54 AM
   Lease Expires . . . . . . . . . . : Wednesday, October 08, 2014 12:08:32 AM
   Default Gateway . . . . . . . . . : 10.100.30.1
   DHCP Server . . . . . . . . . . . : 10.100.20.100
   DHCPv6 IAID . . . . . . . . . . . : 237270787
   DHCPv6 Client DUID. . . . . . . . : 00-01-00-01-17-CA-29-8A-D0-67-E5-54-28-5C
   DNS Servers . . . . . . . . . . . : 10.100.20.100
   Primary WINS Server . . . . . . . : 10.100.20.100
   NetBIOS over Tcpip. . . . . . . . : Enabled
Ethernet adapter Local Area Connection:
   Media State . . . . . . . . . . . : Media disconnected
   Connection-specific DNS Suffix  . : klc.local
   Description . . . . . . . . . . . : Intel(R) 82579LM Gigabit Network Connection
   Physical Address. . . . . . . . . : D0-67-E5-54-xx-xx
   DHCP Enabled. . . . . . . . . . . : Yes
   Autoconfiguration Enabled . . . . : Yes