I have 3gs 3.13 and would like to know how to find our what is my boot rom. some say from the serial # and some say from the out side the box. please help me

There are several methods. The "side of the box" method is hit or miss, it CAN be inaccurate. What you're looking for is the fourth and fifth numbers of your S/N. These correspond to the week the device was made, and using deductive reasoning, you can determine whether your phone was made before or after the new iBoot was released. Problem with this is that refurbed phones can have the new iBoot but have an old S/N.

The 100% guaranteed way is the following:

PC
1) Put your phone in DFU mode and plug it into your computer
2) Start Menu -> Control Panel -> Device Manager
3) Under one of the Universal Serial Bus Controller items, you will see Apple Mobile Device USB Driver. Right Click on this and select Properties from the drop down.
4) Go to the Details tab, and select 'Device Instance' in the drop down.
5) You will see [iBoot-359.x] at the end, that tells you the bootrom version.
6) Kick your phone out of DFU mode either by using the home/power combo or using iRecovery/iReb

MAC
1) Put your phone in DFU mode and connect to the PC
2) Run System Profiler
3) Select the Phone from the list and check the details. The iBoot revision will be listed.
4) Kick your phone out of DFU either by home/power or using iRecovery/iReb/etc.

This will let you know your bootrom version, reliably.

Originally Posted by n1ckn4m3

The "side of the box" method is hit or miss, it CAN be inaccurate. What you're looking for is the fourth and fifth numbers of your S/N. These correspond to the week the device was made

You also need to look at the 3rd digit - which is the year, which has to be 9 for 2009. Apple is soon changing it's serial number format (moving to 12 digits) and it will be much harder to work out week number and year (they are encoding this differently in the new serial number format).

As n1ckn4m3 says, it is best to query this directly using the procedure he outlined. If you are unsure about how to Enter and exit DFU mode this thread explains that.