<p>Every project I compile with Delphi 7, in which I do <strong><em>not</em></strong> compile with run-time packages, gives a linker error: "Too many resources". Even a blank application gives this error.</p>

<p>In other words: Delphi died on me.</p>

What happens when you try to build it from the command line?
(i.e., \Program Files\Borland\Delphi7\Bin\dcc32.exe)
Also, have you build any custom .RES files for this project?  If not, try deleting the default .RES that Delphi created for you, and let it get re-created by the project.
You can also force an update to the .RES file by changing something trivial, like the version #, saving your project, then changing it back again.
Sorry these are not answers... but hopefully we will find the issue with a little poking around.