I don't know if you found the answer yet but the exact same thing happened to me. I hope this helps you and anyone else that has the same problem. It was driving me crazy. After many trials and errors and cleaning the system inside and out and searching the internet for a solution, I found out that the problem is with the power adapter.
You need a genuine Sega CD power adapter. I used a universal NES/Genesis 1 power adapter and it does not supply enough juice. I got a genuine Sega CD power adapter and my Sega CD works perfectly now.
I actually have two working Sega CD systems. After I couldn't figure out the problem with my first "working" Sega CD that I bought from E-bay, I went our local Swap Meet and I found a Sega CD model 2, Sega Genesis model 2, Sonic 1, Prize Fighter Sega CD, 6 button controller and both power adapters all for $60.00. I snatched it up.
The man said it worked and he even hooked it up to a TV and showed me. I went home, plugged it in and it had the same problem as my first Sega CD had. From there I replaced my old power adapter with the new one I got with the new system and it worked perfectly! I swapped out my E-bay Sega CD and Genesis combo and it worked too. SWEET!
I hope this helps anyone else who is having these problems. Try replacing the power adapter before doing and modding or tinkering with the circuit board. You might be pleasantly surprised.