I wish to thank the entire XDA community for once-again-manifested total disinterest in dealing with problems of people using Windows Mobile.
After weeks of struggling i have resolved the issue myself by installing the Esmertec Jbed Java client, instead of the one that was pre-loaded in my system.
Now Kayak works perfectly. Hope this will be useful to someone else at least.
PS: Here is the page with the Esmertec Java emulator:
PS2: This issue and solution applies to all versions of Windows Mobile, the reason of initial malfunctioning not being cause of WinMo 6.5 but cause of a different Java client installed in the Rom. After that i've got the same problem on the 6.1 which indicated me that the problem wasn't the system but Java itself.