I just tested the demos in components/turbopower_ipro/examples, and could compile and run each one of them. It is only the browser example which seems to have issues at run time when opening a URL - I must have closer a look when I have time.
So please provide more details: What is your OS? Which Lazarus and fpc version? Are the iPro components installed at all? You MUST be able to compile and run the file-based sample projects (e.g. htmlfileexplorer1). Otherwise something is wrong with your installation.
For migrating a project from Delphi you will probably see issues because the original TurboPower Internet Professional library had a bunch of components while only of few of them have been ported to Lazarus so far.
[P.S.]
The browse example runs with a complete url including file name, such as
http://www.lazarus-ide.org/index.php For this, you must get yourself the latest trunk version of Lazarus, or you replace the line
FContentType := FClient.ResponseHeaders.Values['Content-Type'];
of TIpHttpDataprovider.CheckURL in Iphttpbroker.pas by
FContentType := AllTrimSpaces(FClient.ResponseHeaders.Values['Content-Type']);