Bluecow,
If you have cleaned the rifle as detailed by some of the posters and it still does not work, I would suggest a new magazine. If that fails, it may be worn out. The 740 and 742 had durability problems, Remington realized this and did make important design changes between the 740, 742 and 7400 models. Remington used to post the development story with all this history on their site, I cannot find it now. For you, it is only interesting reading. The 742 that I used for high power matches in the late 1970s wore out. I returned it to Remington and they fixed it, but they also warned me it was not designed for such heavy use and that the rifle was approaching the end of its useful life. I sold it to a collector who only cared that it functioned correctly. This may be the course of action you need to take, as they do reach a point where the failure is irreparable.
The following is what Remington Firearms offers on its "Support" forum in the "Help" file, this answer posted by Remington in response to an inquiry about the differences between the 742 and 7400.
The Model 7400 has been completely redesigned. The barrel, bolt, receiver and action bar have been enhanced. Internal parts are not interchangeable between these models. Rear stocks are interchangeable but fore-ends are not. We no longer house parts for the Model 742 which has been discontinued since 1980. If you need parts or service for this model, please check with an Obsolete Parts Dealer.