Learn Spanish (Latin America): Me encantan los tocadiscos viejos.

Tocadiscos is a compound noun made of a verb (tocar) and a plural noun (discos). In Spanish, compound nouns constructed this way are invariable. This means they have the exact same spelling in the singular and the plural. You only change the article and any adjectives, like going from el tocadiscos viejo to los tocadiscos viejos, to show that there is more than one.

Is the first part of tocadiscos the verb tocar?

Yes! Compound nouns for tools or machines are very often formed by combining the third-person singular of a verb with a plural noun. Here, it is toca (plays) + discos (records), creating the word for a record player. Other common examples are el lavaplatos (dishwasher) and el abrelatas (can opener).

Since discos is masculine, does that make the whole word tocadiscos masculine?

It is masculine, but not because of discos. Almost all compound nouns made of a verb plus a noun are masculine in Spanish, regardless of the gender of the noun part. For example, even though las latas (cans) is feminine, a can opener is masculine: el abrelatas. So el tocadiscos follows this very reliable rule.

Why is the verb encantan plural here?