It sounds like the libraries or Windows services involved with those applications are damaged or stopped. In the interests of portability, much of the network modules for Perl may not require the same level of support from the OS as native applications.

You may need to uninstall and reinstall such things as the TCP/IP protocol or start such services as "HTTP", "Client", etc. Even though you clearly do have TCP/IP access from the machine, the protocol packages that Windows uses are at a pretty large granularity. You may also need to either repair or delete and recreate the network connection profile.

Basically, treat the situation as if you have no network connectivity through that interface at all. That Perl can access the Internet through it shows some functionality, but only by replacing parts of the stack can you assure something's not corrupted and offering only that partial function.