Are you sure that's not the problem? Because according to the second code you posted you seem to want to tune to 88Mhz but the code you're sending (0x06 0xE0) is setting the tuner to 88Mhz which means the frequency you'll be receiving is 88-33=55Mhz. If you want to receive 88Mhz you have to tune it to 88+33=121Mhz wich woud be 0x09 0x74.
What you should do is set the tuner to around midway in the FM band (~100Mhz); by tuning the ta2003 you should be able to receive at least two or three stations. I used your code with the same tuner and it worked (of course the frequency displayed in the lcd is incorrect because it doesn't take into account the IF frequency of the tuner) I don't even have the pull up resistors, arduino seems to work fine without them. If that doesn't work, the only thing i can think of is making sure the ta2003 is working at the right frequency (that would be either about 44 or 22Mhz). It would be helpfull if you could post some pictures.