How can I download everything from iCloud to my new MacBook Air?

If you had iCloud Photos, iCloud Drive and other iCloud syncing options turned on in your old Mac, you can turn on those same options in the new one and the data will sync with it. See: Set up and use iCloud Photos - Apple Support and Set up iCloud Drive - Apple Support and Set up iCloud for Contacts on all your devices - Apple Support Other iCloud data such as Notes, Reminders, etc can also be synced.

If you aren't sure whether you had those options setup on your old Mac, use and internet browser and log into www.icloud.com and look for the data there. If the above data isn't there, it wasn't synced.

Apps cannot be synced with iCloud. If you had apps that you purchased or downloaded from the Mac App Store, go to the Mac App Store on your new Mac and download them from there.

Go to System Settings ➜ Apple ID ➜ iCloud and make sure the "Apps Using iCloud" are turned on.

For iCloud Drive, if you had Documents & Desktop turned on, on the old computer, then turn it on there too to sync the files down.

For other files, just open Finder, and look in the iCloud Drive section.

Beyond that, if the only issue with the old computer is the keyboard, you can connect an external one. what exactly do you mean by "the keyboard is fried"? Keyboards don't normally fry, unless you do something to them.

FoxFifth gave an excellent overview of how to recover any data that was synchronized with iCloud.

Even if you were using iCloud, it's quite possible that some data wasn't synchronized through it. E.g., files in your Documents folder would not be in iCloud, unless you were using iCloud Drive and had chosen to synchronize your Desktop and Documents folders through iCloud.

If you have a Time Machine backup, or bootable clone backup, of your old computer's startup disk, you can point Migration Assistant on the new Mac at that disk, and have it migrate from that disk. The restored data will only be as up-to-date as the backup was, but you won't be locked out of using Migration Assistant just because you can't make a working cable connection to the dead computer.

If you have a non-bootable backup (other than a Time Machine backup), you can still use that to recover data, but you'll have to do that manually. Migration Assistant only wants use Time Machine backups and startup disks.

I don't want to hold out false hope, but if your dead MacBook Air has a model year that falls between Late 2010 and Mid 2017, it may be possible to have a repair shop pull out the internal SSD and put it in an external USB enclosure. (OWC carries enclosures for factory SSDs for MacBook Airs from those years. They'd probably know about as well as anyone if any of those SSDs require special enclosures.). Then you cross your fingers and pray that you can read the drive – maybe even migrate from it. (Whatever killed the Mac may have killed the drive. With hard-drive-based Macs, it's often the other way around: the death of the hard drive is what kills the Mac!)

Gonna say the coffee.

Try an external keyboard, USB.