Let me try to address each of your statements-
I had an old computer that broke and I couldn't get the current catalog from LR Classic off it.
If it's "broke" then you cannot recover a Catalog from the old computer (maybe an internal Drive, if it is still working). You can only recover a Catalog from a Catalog backup, AND original photo files backup, you have made to another working physical drive.
This catalog was synced to the cloud.
How? You can only Sync photos in LrC Collections. You do not sync a 'catalog'. And photos synced from LrC Collections only are placed in the Cloud as Proxy files (aka Smart Previews), not the 'original' files.
I logged in and the old catalog is there.
Where? On the iPad? Well that is NOT the Lightroom-Classic Catalog! It is a Lightroom (Cloud) catalog. A totally different thing.
A new catalog on your computer, with Sync turned on, will atempt to download files in the Cloud catalog that are 'Original' files. Any files that you synced UP from LrC Collections may be lost permanently (unless you do have the full-size backups on a local drive.).
So, Have you recovered all photos and a LrC Catalog from a Backup saved from your broken computer? You are going to need more advice to restore your unfortunate mess.
Regards. My System: Lr-Classic 12.3 Photoshop 24.3, ACR 15.3, Lightroom 6.3, Lr-iOS 8.0.8, Bridge 13.0.3, Windows-11.