There's nothing wrong with the fixture. I retrofit fixtures like this all the time. In fact, a good, stout old fluorescent fixture is better than any of the new replacements made out of flimsy sheetmetal.
However, the Ballast has failed. And this is time for an upgrade anyway. This is an old "magnetic" ballast, which works with specialized transformers. To keep the transformers from buzzing, they fill the ballast with tar. The aging transformers run hotter, melting the tar until it leaks out.
There's nothing wrong with the wires, they were just dipped in tar. You can clean it off the wires with paint thinner and patience if you really want to.
Other than that, you can disregard the tar.
The "electrical tape splice" is terrible workmanship and you will be replacing it with a proper splice - a blue or orange wire-nut should suffice.
Decide what kind of fluorescent tube you want to use going forward:
- What you have now, fluorescent T12, is obsolete and tubes may become scarce. Color quality is absolutely superb, as high as 98 CRI, because the gov't outlawed all low-color-quality tubes in an attempt to run T12 off the market.
- Fluorescent T8 is the latest of fluorescents and performs well and CRI is also top notch (90-98). I recommend rapid-start or programmed-start ballasts as the wiring will match. Instant-starts will be confusing to wire.
- Direct-wire LED is the up-and-comer, but CRI isn't quite as good (typically 70-80 unless you are a very finicky buyer).
- Do not use plug-and-play LED. Those require ballasts and yours is dead.
Historic fluorescent tubes have a CRI around 35.
Once you decide on the tubes you want, pick the ballast you need (none for direct-wire LED, T8 ballast for T8 tubes, T12 ballast for T12 tubes). Don't be surprised when the new ballast is a feather compared to the old one.
Turn off the circuit, cut the wires right at the chassis of the old ballast, remove the old ballast and fit the new one. We describe wiring diagrams in other questions on this site. Then fit the new tubes that match the ballast, and enjoy the new light!