Installation finished fine but it doesn't work.

I am new to WordPress but familiar with the technology. This is a new install to my own local machine. It has mySQL, PHP and Apache all running fine, as a test environment. I followed the instructions and everything worked fine during the install. I installed to the folder /wordpress.

Problem 1 – doesn’t run dashboard after login.
At the end of the install it asked me to login. I did. It then displayed the list of files in /wordpress/wp-admin but did not run the index.php file that is there.

I have tried running /wordpress/wp-login.php and that askes me to login. If I enter the correct details it does the same as above, just gives me the list of files.

I can then run /wordpress/wp-admin/index.php and it takes me to the dashboard, which appears to work.

Problem 2 – can’t run WordPress itself.
If I run /wordpress/index.php nothing happens at all.

Problem 3 – can’t change header image
In the Dashboard, I went to Appearance/Header/Upload image. The Browse for the file works, the upload works, but when I press “Crop and Publish” it says “Image could not be processed. Please go back and try again.” My image is a GIF file 600 wide 80 high.

If I change something else in the header, such as removing the image, it says “Header updated. Visit your site to see how it looks.” and if I press “Visit your site” it shows me the list of files in /wordpress

Help
I suspect I may have something wrong in the Apache configuration, but it works perfectly with a php/mySQL application I have running.