I'm not certain, but I would think that not having the transponder would not even allow you to crank it? That might imply that you actually do have a transponder key without the remote FOB I assume, or your transponder security unit has somehow been bypassed? Post a pic of your key. You can try to wrap your key plastic in a few layers of tin foil and then try to start the car. You may find it does not even crank this time.

If it won't start but it cranks, it is usually either spark or fuel. You would need to check for each with basic tests. Check the ignition, ECM and fuel pump fuses also. However it can be other things sometimes too like a bad camshaft or crankshaft sensor. Can you try to pull OBDII codes if there are any?

It may be a good idea to do a visual inspection under the hood (or have one done by someone experienced) and the fuses as already mentioned. Maybe someone removed parts from the car?

If it was sold at auction, did you not drive it off their lot or see it running?

 

Do you know what trim of Camry you have? Cars with a transponder chip usually will allow the car to start then shut off if it can't detect the key OR it'll just crank crank crank.

As far as I know, the LE trim Camry do not have a transponder chip. Not sure about the XLE trim Camry.

It could also be caused from the RS3000 that might be preventing the car from starting if the alarms been triggered. Maybe the engine timing is off or something.

 

Maybe the engine timing is off or something.

Maybe even a broken timing belt?! OP, you would have to check for that by removing a valve cover of course, but check the easier things first as already mentioned.

 

Some aftermarket immobilizer setups will be cancelled if you turn the key on until you get red dash lights on and leave it in this position for half an hour
I don't understand how it works but the locksmiths told me to try it with my 1993 model Camry and it was successful

 

Call a mobile locksmith that can cut and program the key for you onsite. Get a quote first obv, but I bet it'll be cheaper than the stealer.

 

Did the '98 Camry even have a transponder chip ? ..

The (US) '00 Camry here doesn't, aftermarket keys work fine: same setup w/ remote key-less entry & fob.

OP can confirm installed options by visiting a Toyota Dealer Service department and providing VIN, that's what I did here.

+1 for checking the Timing Belt first.

 

If an ES of this time did not have a transponder, I highly doubt the Camry does. I?ve not come acrossany Gen4 with it... even the XLE one. ... again unless this Camry is an XLE one which is uncommon

 

My 2001 LE had a transponder, if the various parts listings are to be believed some 1998 models also had it google 89785-26020 which is a transponder key. If you look at this listing you can see what looks like a transponder module.

https://www.ebay.com/itm/162678311176