This TV has been doinghtis for years and was given to me. I would not
mind taking it to a shop but it is very heavy and my wife is expecting
a baby any day now.

Is there a way I can "attempt" to do this at home?

I wouldn't recommend repairing it yourself, especially if you have no
experience soldering and/or if the set uses an inline tuner module which was
known to develop solder joint cracks for the tuner grounds.
But, whether or not this set has an inline tuner or not depends on the chassis
number, which is followed by a CTC prefix. This important number is printed on
the lower right hand corner of the rear label for the television while the
lower left hand corner has the model number of the set printed on the same
label.

If the set, according to its CTC number, has an inline tuner module, it is
highly recommended that you call a reputable repair professional and ask if
they can perform an in-house repair.

Continued use of a Thomson set with bad solder ground connections in the inline
tuner module with chassis so equipped with it can eventually damage the system
control EEPROM, which will require a much more extensive and expensive repair
to fix provided that parts are even still available for it. - Reinhart