No Internet access when switching IP's

I just checked the Event Viewer, and found an event log (ID 4624) with Wifi IP of when the user switched from Ehternet to Wifi.

An account was successfully logged on.

Subject: Security ID: NULL SID Account Name: - Account Domain: - Logon ID: 0x0

Logon Type: 3

Impersonation Level: Impersonation

New Logon: Security ID: Domain\USER$ Account Name: USER$ Account Domain: Domain Logon ID: 0x159B748D Logon GUID: {00000000-0000-0000-0000-000000000000}

Process Information: Process ID: 0x0 Process Name: -

Network Information: Workstation Name: Hostname Source Network Address: 192.168.X.X Source Port: 50941

Detailed Authentication Information: Logon Process: NtLmSsp Authentication Package: NTLM Transited Services: - Package Name (NTLM only): NTLM V2 Key Length: 128

This event is generated when a logon session is created. It is generated on the computer that was accessed.

The subject fields indicate the account on the local system which requested the logon. This is most commonly a service such as the Server service, or a local process such as Winlogon.exe or Services.exe.

The logon type field indicates the kind of logon that occurred. The most common types are 2 (interactive) and 3 (network).

The New Logon fields indicate the account for whom the new logon was created, i.e. the account that was logged on.

The network fields indicate where a remote logon request originated. Workstation name is not always available and may be left blank in some cases.

The impersonation level field indicates the extent to which a process in the logon session can impersonate.

The authentication information fields provide detailed information about this specific logon request. - Logon GUID is a unique identifier that can be used to correlate this event with a KDC event. - Transited services indicate which intermediate services have participated in this logon request. - Package name indicates which sub-protocol was used among the NTLM protocols. - Key length indicates the length of the generated session key. This will be 0 if no session key was requested.

The IP change detection relies on DNS.

Lets say you're wired at WORKSTATION01.domain.local using 192.168.0.2 and then you switch to the wireless IP 192.168.1.2. The DNS record must be updated in order to detect the change. 

Take a look at your DNS configuration, specially dynamic updates.