Have kenwood vr309 reciver an when power on my display lights wont come on

Into the tape input and tape output RCA plugs

This will all depend on the age of the equipment and what connectors are on each one. Could you post photos of the panels on them showing what connector ports are actually there. How old is the reel to reel? The really early 1970's models will probably not work or will need specialist cable adapters to get it to connect to the Kenwood and even then it may not work. The 80's and some of the 90's ones used Component, Phono or Jack Plug connectors. The really modern ones use Optical cables.
In general it usually sets up by connecting to the "OUT" port on the reel to reel and the matching "IN" port on the Kenwood.

This is usually an indication that the power board has a bad component and the signal wont switch on. The problem is usually related to capacitors and unless you want to replace the whole power supply (if you can find it,) the repair is down to the individual components and it technical in nature requiring troubleshooting gear and soldering skill

check and test the circuit for damage short or overheating

Check the speaker protection circuit first. Make sure the proper sized speaker wire is used and in good condition. Your speakers may be failing electrically too.

well its preety old but if in good condition you could get anywhere from 220-300$if all acessories like control and antennas are included

Here's the manual.

http://www.kenwoodusa.com/UserFiles/File/UnitedStates/Home/Manuals/VR309.pdf

more than likely, there may be some bad solder connections inside of the radio.

Are you sure the VR309 is sending a signal out through the sub port? Attach one of your other speakers to it as a test (low volume). Then get back to us.

There are such things as user settings that affect this.

Please update your post with any Model Numbers that you can retrieve, especially the subwoofer. Off hand, and with the limited amount of information that you have provided, I would GUESS that your subwoofer is simply overheating, and is being shutdown internally, hence protecting the fuse because no short is detected. If you haven't moved and or vaccuumed/cleaned around or near your system regularly, dust, pollution, pollen...you name it, builds up and can easily prevent electronics from breeathing/venting properly.