In MS Project 2010, is it possible to show the entire predecessor path driving the start of one specific task in a Gantt Chart?
Sadly not built-in to Project 2010. It is in Project 2013 through the "Task Path" feature. You can create your own Task Path Manually.
Add the Marked field (or a flag field) to the Gantt table. Using the Task Inspector you can view the driving predecessor to the selected task. Set the Marked field to "yes" for the task and "walk" you way backwards in the file using the predecessor hyperlink in the Task Inspector. If you have used the Marked field, you can then apply a highlight filter to show all marked tasks.
If you want to add different colors to the actual Gantt bars you can accomplish this by creating a new bar style and setting the "Show for....tasks" to marked. If you need more detailed information, post back and I'll go a bit deeper.
You can do this easily if the specific task you are interested in is in the critical path. A short video demonstrating how to do this is at https://www.youtube.com/watch?v=x2nfc3-7Cc8
Thanks for the answers. I was able to view the path for a specific task (non-criticle path) by adding a text column and manually entering the unique ID for the task of interest in each of the prececessor's task lines, then filtering on that column & UID. Kind of clunky and a little time consuming, but it got the results I was looking for.
"If you can't beat the system, trick it."
I have used the freeware "trace" vba macro to perform this task. Available at: http://masamiki.com/docs/trace-task-dependencies.html