Mac OS X 10.5.8 desktop cannot connect to the internet

Mac OS X 10.5.8 Leopard is much too old to make the secure connections required for the modern internet.

There aren't any browsers available that can get the job done in that obsolete OS.

Internet security has evolved a lot in the sixteen (!) years since Leopard was last updated.

The oldest macOS that can still make any secure connection is probably 10.11 El Capitan.

MacOS 10.15 Catalina can, but more and more these days its version of Safari fails to connect. For user still running Catalina there is still a supported version of Firefox.

In 2015, researchers discovered that Secure Socket Layer (SSL) Internet encryption was not nearly as secure as was thought, and needed to be replaced. Internet encryption quickly moved to Transport Layer Security (TLS) which was rapidly deployed across the Internet. Over time, sites tightened requirements for what was acceptable for encryption.

Apple issued Safari version 9 in 10.11 El Capitan version of MacOS, which included TLS encryption. It was later provided by Security Update into the two previous versions of MacOS. 10.10 Yosemite and 10.9 Mavericks, PROVIDED you applied all available software updates.

MacOS versions older than those can not make a lot of secure [httpS:] connections on the Internet, because by todays standards, your proffered SSL encryption is considered inadequate.

While the https security change is an obvious show-stopper, it is not the only one.

The means used to present content on a Web page, once you make a connection to it, have also undergone many changes. The browsers available for Leopard would be likely to format many modern sites incorrectly even if they could connect to them.

The site below does not require encryption. it simply tells you whether your time is accurate according to Internet time, which is also required (within five minutes) to make any secure connections.

http://time.is

if you get a report of your time, the internet is there, but ...

... you can't have any (with your current Browser's encryption)

This is an extra desktop that I would like to connect to the internet.

Which model Mac desktop is it?

Find your Mac model name and serial number - Apple Support

Please do not post its serial number.