I have a JVC 13" the screen goes to a thin line,

Hi dukedms,

Yes the problem is bad solder joints(cracked/dried/cold solder) like what Donald DCruz said. I will add only that the suspected section is on the vertical deflection circuitry most likely the vertical IC. This IC heats up upon operation that's why the solder joints dried or cracked after a few years. This IC is located near the flyback transformer and mounted on the heat sink. Usually this IC has a part no. start from LAXXXX, TAXXXX, TDAXXXX (XXXX means number). Locate it on the board and resolder the joints to resolve the issue.

Hope we helped you.
Have a nice day!
Jdvillanueva

This is purely a DRY SOLDER JOINT on the mother board. The fault can be found our if you can use a good light and observation lens , use a good soldering station to redo the solder on drive IC's and power circuits.