I changed the starter on my eldorado but it is still only making a clicking sound what else could be the problem?

These cars did have problems with the antitheft system. When this system fails, the car "thinks" it is at risk for theft, and disables the starter. I would look into this before you change the starter. This link explains.

http://vatspasslockpasskeysecurityhelp.yolasite.com/

Clicking sound ? loose connection , bad battery or battery cables . Do a voltage drop test on the starter circuit . Do you have an know how to use a DVOM - digital volt ohm meter ?
How to voltage drop test starter motor circuit
Starter Voltage Drop

Since taking the starter out is a real pain, have the battery tested first, most auto part stores do it for free

the clicking is most likely your battery if it was a winding sound its the starter charge or if it doesnt hold a charge get a new battery

Replacing the starter is labor intensive. You access it from under the car. I'm not sure of which engine you have in your Eldorado. But before you change the starter make sure it's not the battery or a relay. The clicking sound is usually a battery or relay problem.

If the battery is fully charged but the starter is slow, the starter may have an internal short or may just be worn out. Make sure your battery is fully charged and the battery terminals are clean and tight though before buying a new starter.

sounds like a bad starter soloniod or a bad ignition switch .. most likely the solonoid if it hasnt been changed ... below is what it looks like and a couple places it can be purchased ... usually the contacts inside the solonoid wear to the point they just barely make contact .. sometimes they dont anymore ... on some solonoids you could just take it apart and rotate the contact so that unused contact area is now seen by the contactor ... .. the contacts are part of the bolts where power is connected ... a new solonoid isnt expensive so is probably the best bet ... if the contacts are worn then you will hear a click when you turn on the starter ...if yoiu dont hear a click then there could be an open coil in the solonoid or maybe a bad ignition/starter switch that operates that solonoid coil ... there are ways of junping the solonoid main contacts .. in this case the starter will run but not engage (you will get sparks) .. at least it checks the starter ... the other way is to provide power to the solonoid coil .. this should cause it to operate and engage the starter (make sure car is in park) .. if that works then suspect the ignition switch .. if it doesnt work or works once in a while then change the solonoid ...

photo of part and availability:
http://shop.advanceautoparts.com/webapp/wcs/stores/servlet/product_x_18970448-P_x_x?cm_mmc=CSE-_-Google-_-VALUE3-_-VALUE4&ci_src=14110944&ci_sku=18970448-21861&vehicleId=21861

another view:
http://www.partsgeek.com/gbproducts/WC/2832-01029316.html?utm_source=google&utm_medium=ff&utm_term=1985%2C+1992-1993+Cadillac+Eldorado+Starter+Solenoid+New+Era+85%2C+92-93+Cadillac+Starter+Solenoid&utm_content=YN&utm_campaign=PartsGeek+Google+Base

Sounds like the temperature sensors. I believe there are 2 on the intake manifold. This tells the computer when the engine is cold so that the computer can adjust for a cold start. I have had to change these several times.

If the starter was an issue, the engine would not crank.

I don't think you need a battery. Check the battery terminals for corrosion and make sure that they are snug. The clicking sound you hear is the lack of voltage going to the starter solenoid. This could be attributed to a poor connection of a wire, or a starter relay in the fuse panel. There are no special tools required to remove the starter but you can have it bench tested at any Advanced Auto Parts free of charge. Good luck

the easiest way to locate your starter is follow the positive whire from the battery down to where it connects to the starter, it is the main red whire from the battery. and make sure you disconnect the negative cable from the battery before you change the starter.