Just google "installshield error 1628" and search for solutions within the last one month and you can find three or four fixes for resolving it.
But before trying any of those, try to install the program as an administrator and check whether it gets you through. Open the CD Install, right click on the specific installer and "Run as Administrator".
If it does not resolve the problem, then try the other fixes.
(Incidentally I too have a Liteon iHBS112 BD writer and had installed the BD Solution on my 32bit OS. Hadn't experienced any install problems.)