Do some basic troubleshooting and post the results and then someone
might be able to point you in the right direction if you still are not
sure which way to go.
Some things you need to post:
What happens when you change channels in the fault condition?
Does the A/V inputs work (if it has them)?
Is the OSD also dark?
Describe how the sound gets weaker, does it just fade away or does it
start to get staticy and distorted?
... and any other troubleshooting results.

The repairfaq has some common faults on some older Sony sets you might
want to look at. www.repairfaq.org