91 Rodeo Starter problem

My 91 Rodeo V6 has been garaged since last winter. Replaced the battery yesterday and it started right up. It ran for about 30sec and quit. Now it won't start, the ignition just "clicks". Did I fry the ignition, starter or alt? Please let me know if you have any ideas. I need to get it running again. Since I am a novice home mechanic, is it a big job to replace any of these things or am I better off just taking it to a shop?
Thanks.

Also, is there a simple method to individually check each of these components so I know what to replace.
Thanks again!