migration assistant cannot find old computer

Migration to a new Mac:

Move content to a new Mac - Apple support

Transfer to a new Mac with Migration Assistant - Apple Support

Migration Assistant 'takes over' both computers, and takes a surprisingly long elapsed time. First it may need to compute a Spotlight index of the data. Once data transfer begins, it takes a bit longer than a FULL backup, likely all afternoon to overnight. You may want to set this up late in the day and let it run overnight, and be ready for it not to be done by morning.

"the best way" is to use your Time machine backup from the old Mac as the source for Migration Assistant running on the new Mac. USB-2 is as fast as almost every Rotating Magnetic drive, and will not produce a noticeable slowdown doing this transfer.

The way that always works but will seem really slow is using Wi-Fi through your Router.

If you could use Ethernet through your Router to BOTH Macs, that would be much faster. OR, if your old Mac is running 10.12 Sierra or later it can establish an Ad-hoc private Wi-fi connection to the new Mac when placed near the new Mac and both running Migration Assistant.

If your old Mac has no Thunderbolt-3 ports, Thunderbolt Bridge is off the table.

A USB cord sounds like a great idea, but does not work because USB is a local peripheral interface, and a Network interface is required, unless you can make your old Mac 'look like a drive' to the new Mac.

Target Disk Mode can allow your old Mac to become a Hard drive, and it can be cable-connected to the new Mac. It requires ThunderBolt cable connection, so for a Thunderbolt-2 old Mac, you would need to obtain a Thunderbolt-3 <-> ThunderBolt-2 adapter (US$50) and a Thunderbolt-2 cable.

Transfer files between two Mac computers using target disk mode - Apple Support

Transfer files between two Mac computers using target disk mode - Apple Support

The old computer needs to be running its own version of Migration Assistant, or be set into Target disk Mode and connected with the appropriate cabling.

if you need visibility into what the old Mac (with broken screen) is doing, connect it to your TV set with an HDMI cable.

You can connect an external display to the older broken Mac in order to see what is going on.

Now are you using Setup Assistant to perform the migration, or do you already have a macOS user account on the new Mac and you have actually launched the Migration Assistant app on the new Mac? I recently had issues migrating between two Macs and found that with Setup Assistant it was not possible to connect with the old Mac when the old Mac was in Target Disk Mode. From some quick searches at the time, I saw others had the same issue. If you are already booted into a macOS user account on the new Mac, then it may be possible to use Migration Assistant to access another Mac in Target Disk Mode as suggested by @Grant.