Things I'd consider doing.
Run a coaxial cable from the transceiver to a remote antenna. Remote is a relative term. If your antenna is within 5 ft of the computer then move it 10 or 20 ft away. The antenna is one pathway for the RF from the computer to get into the radio. The wire connecting the antenna to the transceiver is another. The coax has a braid that sheilds the antenna wire, in a manner of speaking.
Make sure the transceiver is well grounded.
Any other wires to/from the transceiver must be protected - they can be antennas too. Power supply wiring could be filtered for RF but make sure the filter is right at the transceiver.
Is the transceiver itself well sheilded? If you took any cover off, put it back on.
The various wires to/from computers behave as antennas. You can purchase snap on ferrite cores that help attenuate RF that is crawling along the cables.
These are the things I'd do, one at a time, to see if the problem can be solved.