Hori the link you posted is for the LM335 series not for the LM35 they are different.

Here is the manufacturers product page http://www.national.com/mpf/LM/LM35.html
You need the LM35 in a TO-92 casing. The letters behind the label LM35xx are just different models with different accuracy and other characteristics and of course different price.
LM35DZ, the cheapest one will work fine.

Any other casing (except TO-92) of LM35 will work but the size and shape of the sensor does not help for proper installation.

Try to re-solder the sensor, and run it for some hours, it might work.