This is just a documentation of my experience. Maybe one day someone interested might see what caused all this. I am not the only member here to experience some or all of these errors.

First there was the old:
Check that certain classes haven't been defined by PHP plugins Your version of PHP has defined some classes that conflict with SilverStripe's. The following classes are at fault: HTTPResponse

Fixed this by renaming all instances to something else like; SSHTTPResponse

Second was:
Warning: fopen(/tmp/silverstripe-cache-home-thesite-public_html/manifestClassParse-_home_thesite_public_html_cms_code_AssetAdmin.php) [function.fopen]: failed to open stream: Permission denied in /home/thesite/public_html/sapphire/core/ManifestBuilder.php on line 398

Fix this by manually creating directory; "silverstripe-cache"

After all that I have:
[Warning] HttpRequest::__construct() expects at most 3 parameters, 5 given
GET /?flush=1
Line 112 in /home/thesite/public_html/sapphire/core/control/Director.php

Still no joy with the SS installers :(

That error would be because you have renamed SSHTTPResponse but thoughout the code it still uses the php one (which has different constructors). You would have to rename all the occurrences to SSHttpResponse for that to work.

See the ticket here http://open.silverstripe.com/ticket/2827 for the discussion. Not sure if any better solutions are listed among those

Thank you willr. I have re-installed SS so many times that I just gave up in the end. Now I've already installed Drupal(very easy) and started customization. :( I will try SS again one day maybe. Thanks for the help.

Please read some of the comments here to see what others think of SS:

http://php.opensourcecms.com/scripts/details.php?scriptid=61&name=SilverStripe