2003 Accord key fob
 

Will removing the fob battery, still allow the key to start the car? I don't want the trunk to open when I sit on the fob when it is in my hip pocket and I can't see my car.

Your key will start the car with the FOB battery removed.

The chip in your key that allows the car to recognize the key doesn't use the battery.

2003 Accord FOB
 

What type of electronic component is imbedded in the valet key, which is not battery powered? Per the Honda manual, how can the ignition immobilizer detector be potentially confused when the correct key is inserted in the ignition but another car's master key is on the same key chain? Doesn't every husband and wife, with two cars, keep both car's keys on their one key chain?

There's a transponder type chip inside the key. Due to the ID code, the car's computer will not get confused just because there is another different car key nearby. It's a similar concept to security badges with transponder chips or a car toll transponder that some states have.

Here is a link describing the Immobilizer on your year Accord:

http://www.tegger.com/hondafaq/tsb/accord/x02-053e.pdf

Unintentional FOB activation
 

I was sitting in a restaurant with my keys in a leather holder and in my hip pocket, when I looked out the window and saw my, key locked, trunk opened. I panicked because my $11,000 bicycle was in the trunk. Unbelievable my butt never caused this problem in the 10 years I have owned the car. I have now removed the battery fron the FOB, which I never used anyway.

Accord Immobilizer
 

The Honda manual say's not to have another car's key near the ignition switch, before inserting the correct key. Is the ignition immobilizer transmitting, before you insert your car key?

You have three threads essentially on the same topic, so I merged them into one thread.

I think the immobilizer in the car will only search when a key is inserted into the ignition switch and turn it to the II position.

I'm not sure if the key continuously transmits a signal.

Although the manual warns not to have another car's key near the ignition switch, in practice, there usually is no problem. It is a warning that it may cause problem(s).

As stated in the pdf link provided above:

Immobilizer Control Unit-Receiver
The immobilizer control unit-receiver is inside the bezel around the ignition switch. It uses electromagnetic induction to energize the electronic circuits in the key. There is no direct electrical connection. Once the electronic circuits are energized, the key sends its ID code to the immobilizer control unit-receiver, which checks the code against the codes stored in its memory. If the code matches, the immobilizer control unit-receiver sends a unique serial code to the ECM/PCM. But if the transponder ID code does not match, no serial code is sent.

Even on the Honda S2000 with push button start, a key is still required to be inserted into the ignition and turned to the 'ON' position before you can start the car by pressing the start button.

Accord Immolbilizer
 

Ok, I give up. In what circumstances could another car's key or a metal object confuse the ignition immolbilizer, before the correct car key was inserted into the ignition? No matter how unlikely, wouldn't it be possible for this to happen, if Honda say's to avoid doing this?

I've had other keys nearby without any problem. When we had 3 Hondas, I had all 3 valet keys on one ring so I could use them to move cars around the driveway when the kids were too lazy to do it themselves.

The component inside the key is called a "RFID tag" (google it). It gets power from the radio signals coming from the immobilizer antenna inside the steering column. The keyfob battery is only for the remote-lock transmitter.