Hello,
Please note that BY DEFAULT, Microsoft Project 2010 now schedules MANUALLY --- this is different from its behaviour upto 2007, wherein it was AUTOMATIC. Most new planners (new to 2010, not planning) are generally not aware of this, or choose to ignore the message that says you are in manual mode.
When you are in manual mode, ALL your tasks are created manually. Changing a start date, in this case, DOES NOTHING.
What you need to do is:
1. Press Ctrl - A (when in your task) OR click on the TASK NAME heading to select ALL tasks
2. Select Automatic as scheduling method.
3. THEN change the start date.
Project 2010 will now RE-CALCULATE it from the start.
Note that if you have LINKS and CONSTRAINTS, those tasks may turn up wonky. But like someone below mentioned, if you have a CLEAN COPY (namely, only tasks, when they start and how long they are --- minus the links and constraints --- and you SHOULD always have a backup that way), then you should not face any issues.
Hope this helps.
Thanks and Regards,
L H