Why can't the F-22's computer/sensors be replaced with those of the F-35?

Maybe not. The F-35 avionics were designed differently than most aircraft. Most aircraft have a bunch of avionics boxes in the electronics bays and each performs a single function (or a couple). For a radio like the Fighter Data Link, aka Link-16, you have one box that has a receiver/exciter, and a power amp, and maybe a crypto card from NSA that does encryption. This connects up to an avionics bus (Mil-Std-1553C) that lets the pilot control functions from his MFD - multi-function displays. There are a lot of these boxes for comm, radar, nav, fire control, etc. You can generally upgrade each individually.

With F-35, they built an CNI system that is a big rack with a bunch of cards in it. Each card performs one or more functions, and Northrup did the entire box and the software (with some help in specific area). Maybe that save some time or cost - maybe not. But each one of those elements in the CNI system are pretty much owned by Grumman and only they can work on them.

It may come that someday the cost and capability of the F-35 will be adapted to the F-22 - the F-35 is a new program, there are a lot of copies of it, and it will get a lot of upgrades. And there are cost saving in logistics and training that could make combining them cost-effective.

F-22 lacked the standard Fighter Data Link that F-15s, F-16, F-18, and other combat aircraft use to share information - it’s their “internet”. This was left out for stealth reasons - Link-16 transmits on UHF constantly and it would be easy to detect in the air. It was replaced by a very direction link called MADL - multifunction advanced data link - that use radar frequencies to send a beam to another aircraft. To bridge the Link-16 to MADL aircraft, a relay aircraft called BACN is use - basically a commercial jet with a lot of radios onboard.