I would say you are right, there are likely bad electrolytic caps. On something of this age I always replace all of the capsbefore doing further troubleshooting work.
A good test tool is a short checker lamp in these instances when powering up unknown condition equipment....put a 60 watt bulb in series with the power line to the device...if it glows briright and stays bright you have a short and this will protect the device under test from overcurrent.
Working on TV's can be dangerous if proper safety precautions aren't followed...make sure you are familiar with these procedures before commencing repairs.
Check out
www.repairfaq.org for good information on TV repair safety.
One test you can do is to hook up your short check lamp to the TV with the rectifier tube out. Check and see if your other tubes light up including the CRT. The test lamp bulb should glow dimly and the tubes should light.