how can i pair my old iMac battery trackpad to my newer imac

You offer no details on anything; that makes offering a solution merely a guess.

If the old trackpad is BT capable, you pair it exactly as you do all other BT devices. https://www.makeuseof.com/tag/how-to-turn-on-bluetooth-on-mac/

But depending on how old it is, it may not be BT. Have you confirmed it's a BT device? Using its model number and make, that may be stamped somewhere on the device, you can search the web for the maker and get the info maybe.

... to the newer iMac which uses....

Which "newer" iMac? Its sub-model and macOS version, found in "About this Mac..." are everything in this matter.

ON the "newer" iMac, you may need to open System Prefs (or Settings) > BlueTooth, and DELETE the lost trackpad it is shows there. Then try pairing the old one.

My 2017 iMac running Mojave has no issues with my battery-powered Magic Trackpad I bought in 2010.

Wi-Fi has nothing to do with Bluetooth. They are two completely independent capabilities

My earlier comments stand.

Non functioning Wi-Fi is not in your OP and it's a completely different situation requiring a completely different approach.

No, working Wi-Fi means you can navigate the internet and access your local network.

Wi-Fi is not needed to do local non internet, non network tasks. With the exception of those apps that need the internet (mail, browsers and etc) your Mac will use all its apps without the internet.

If that's not the case, either your Mac itself, or the OS, is damaged ... or both.