I am using libreoffice-build 188.8.131.52 on Vista sp2 32 bit machine. In Writer, Calc, and Impress when I have a graphic selected the Drawing Object Properties Toolbar turns on as expected. The Arrow Style button shows as active when pointed at but does nothing when clicked. The Arrow Styles are available in the Line dialog box so it is not a big problem.
I can't reproduce here with beta 2, sounds though like some obscure configuration problem, can you make sure any old openoffice configuration and even the current libreoffice configuration profiles are inaccessible in order to test this?
E.g. you would need to move the .openoffice.org, and .libreoffice directories to a temporary location to test ( or you could delete them if you to lose and local custom ui config changes etc. )
I am pretty sure that this one is a DUP
Please feel free to reopen this Bug if you find out that your problem differs from the one in Bug 32676
*** This bug has been marked as a duplicate of bug 32676 ***