I have no power to my 19 inch sylvania flat screen

I'm going on the assumption you are not a television technician in which case your ability to troubleshoot the problem will be very limited
. If your television is still under warranty, you will void the warranty if you attempt any repairs.
Tthe first thing you want to do is be certain the outlet the television is plugged into is working. Don't assume because one outlet in a duplex receptacle is working that the other one is also, verify it by doing a voltage check, or at the very least plugging in a lamp.
I hesitate to give anybody advice about working on any product that has capacitors.
If you don't know why I would say that, I think you will be taking a chance of hurting yourself or ruining your television if you attempt to go any further.
Even if you understand my reason for saying that and the warranty has expired, I can only think of two things you may want to try to do yourself.
1. With the TV unplugged check the continuity of the wires from each prong on the plug to where they terminate in the TV.
2. Locate and check any fuses.
If you don't know how to do those two things, do yourself a favor and take it to someone who does.