Firstly, thank you all for the answers. Now I can see more clearly about the problem.
So, I called the CS again, (since they won't let me talk to the technical support--company policy stuffs) and read them this knowledge base on this page. this time they tell me to delete specific Serv Book. Which is WAP2 transport, WAP browser config, and bbibs2.
We can all agree now that its not the blackberry server side. They, my carriers, stated no problem with their network. So perhaps its my hand held. If something was defunt on the hardware, why can I still able to write this reply from opera. Update my twitter from ubersocial? It can't be my hardware. Seems all normal.
Before going further, I'm using the BB full service data plan of 3 Indonesia which includes full internet service, bbm, but exclude wifi conectifity, video straming and bb as modem. This data plan should gives me access to the use of nAtive browser for browsing, facebook, twitter, bbm, etc. and I only use this provider for blackbeRry. Also I believes they separated their internet data plan wit blackberry data plan. So I have to purchase another data plan tobe able to browse the internet using their internet apn. I never purchased that plan, so if my data plan isn't functioning, I shouldn't be able to browse using anything from my handheld.
So, I decided to look at those specified servbook they told me to delete, (which is sent again after restarting and doing what abhijitbiswas suggesting doing a complete shutdown of my device and turn it on again after 1 minute (adding bonus time perhaps better )
I don't know the appropriate setting of a service book entry, but those that I got seems faulty. 1. The service record of WAP Browser config in the service type and sub-service type defined as "Not Spesified" it has define the gateway address tho. 2 the WAP transport 2 record also define the service type and sub-service type as "Not Spesified" but the gateway use //0.0.0.0:0;0/3GPRS|GPAK
Shouldn't both service type or sub-service type spesified as "Blackberry(r) Internet Service"? Would this be the problem?
I'm planning to go to my carrier's representative office today, perhaps with these suggestion that all of you provides here can "enlight" those people at the office.