While I don't have any idea what the program itself might be, I do know that when a program that has a tray icon crashes, its tray icon remains until you hover the mouse over it. So what ever program it is, is starting and crashing repetedly.
Try looking around where there are programs set to run when Windows starts, and take a look through the list of services as well.
Places to check for startup programs:
- Start menu - "Startup" folder
- Run command - "msconfig", Startup tab
To check Services list:
Open Control Panel, and type "administrative tools". Open the item that appears in the search result by the same name.
In the window that comes up, double-click Services.
Take a browse through the list of services in the window that opens. If you find anything that looks odd, feel free to send me a private message and I'll do my best to help.