Definitely worth repairing. they were built between 1993-1998, so they're 25+ years old; may require some maintenance.
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Omron makes lots of relays. If you are unfamiliar with what they look like on the circuit board just look for a little rectangular plastic box component near the output jacks. It will have a number on it that you can easily google and find a cross-reference number for. Sometimes the number is on the side, the top or the bottom, in which case you won't see it until you remove the relay. The average price is around $12. I have purchased many on Amazon and eBay. They are easy to replace without the need of expensive tools. Just a cheap soldering gun and some solder (lead free) will work, but a desoldering tool with vacuum will speed up the process. The relay is going to be a double pole double throw. Just make sure the voltage is the same (usually 12 or 24V. Relays have contacts inside. Often these contacts wear out or get damaged and no longer close the circuit properly, or do it intermittently, thus the static. Without testing the unit, it is very difficult to be 100% certain that the relay is your problem but based on what you described and the fact that there are no pods (knobs) on that amp and my past experience the relay is likely the culprit. After all it's a cheap part. What have you got to loose!
Page 3 is the schematic, the difference lies in the number of output devices between models.
ST1400 2 Pair/Ch 105 W 8 ohms
I looked at the schematic. Looks like the relay you need is twT9as 24VDC.
Your amp takes two since they are single pole relays. One for the left and one for the right channel. I would replace both while you are at it, since they are electromechanical devices and have a life cycle. The good one is likely not far from giving out also. They are very cheap, and you can find them all over the internet by typing twT9as. Check eBay. Would love to know the outcome! Best regards.