I hope you are learning lots and at the same time pulling your hair out
First I want to tell you that I am not an expert with this stuff and I am getting to the edge of my knowledge.
In my opinion IE is freezing the whole access program. I cannot get the timer to fire at all when working with your DB.
By the way to find the window as I said in a earlier post the name of the window is important. For example I am home now on Vista with IE8 and that window is called "message from webpage" you are going to have to deal with all these names.
I think your options are to either give people a form in access on which is the webbrowser control.
The second option is you are going to have to build an .exe file which is not that hard for your timer.
I built one in VB6 which I still have but you could do it with VB.net express.
It is exactly the same code only in an exe.
Then you fire the .exe
hit the login
.exe will fire because it is a totally different program on a different thread.
as soon as the dialog is gone your access code will continue.
If these dont work for you, you could code it in another office program like word or excel. I cannot because the work computers have a high security level and any VBA code has to be agreed to each time by the user, but if you can execute VBA code from another office program then your timer could be in the program. All office programs can work invisible except Powerpoint so no one would see it.