I have a 97 BMW 528i... When I put the key in the ignition the lights on the panel blinks real fast and the car makes clicking noises. The car doesn't even start. And from time to time the car alarm goes off on its own.

have your key checked to see if the chip is damaged. if the chip is fine check the reader in the ignition barrel. while you doing this or before or after check the fuse's in fuse box and the main engine fuse in the engine bay inside the black boxes. if you key rattles the chip has come out and you need to have it put back in place. the can come away from the key side inside the key sits next to the key metal.

Make sure it is not the steering wheel lock. Partially turn the wheel while trying key.

have your charging system checked to make sure alternator is charging to specs, also make sure no light are left on, (trunk light ,glove box mirror light.it sounds like you may have a draw somewhere, may be alternator or something is on, hope this is helpful.

My sincere apologies for the delayed response.
I am personally going back to answer your unanswered questions.

I do not know if you still need this information, but I am going ahead and answering it anyway. You may want to Print the Diagrams for future use.

CLICK on the following LINK. It has the Belt Diagrams you will need.
If you would: Before Clicking: Let me know if this helped you, or if you have any additional information or questions. Feel Free to contact me at FixYa.com!
Again my apologies...
http://www.2carpros.com/car_repair_information/year/1997/make/bmw/model/528i/1997_bmw_528i_drive_belt_routing_diagram.htm

check the brake pedal switch 1st. they're notorious for needing replacement.
google: key words: bmw brake pedal switch 1997 528i

then the fuse.

dealer item give the Vin number and they will surprise you with how much ,,,good luck ,,Joe

Flashing light mean something is been tampered with on car, either locks, ignition, radio etc, Had similar problem, could only be reset with diagnostic computer.

BMW engine light

Comes on if DME engine management system self diagnostic fault detected. Will stay on until codes are called up and memory erased.

With OBD read the code as follows. Turn on ignition key, press accelerator pedal to the floor five times within 5 seconds. The check engine light will remain on for 5 sec , blik off, come on for 2,5 sec, go off for 2,5 sec and fault code will begin to flash. If more than one fault exist 2nd fault code will be separated by 2,5 sec pause. after fault codes there will be a 0.5 sec flash and light will remain off. to read codes again do procedure again.

Canceling of codes. make sure fault code is present (short blink and light goes out for long period), depress throttle pedal for at least 10 sec. read fault codes again and check for code 1444 (no faults stored.)

Check also the following, fuel pump, oxygen sensor, fuel injectors, engine coolant temp sensor, idle speed control valve, mass airflow sensor and too many other things.

abs sensor in one of the wheels is dead