Is the network adapter recognized within the guest operating system's Device Manager?

What may be worth a try is to install VMware Tools, which comes with additional drivers that are not included with the default installation of Windows XP. The latest supported VMware Tools version for Windows XP is 10.0.12.

An ISO image can be downloaded from https://packages.vmware.com/tools/releases/10.0.12/windows/
Attach the ISO image to the VM's virtual CD-ROM drive, then install VMware Tools in the guest OS.

André