22J 6KV and 33J 6KV are two kinds of ceramic cap that seems to be burned out. What do I replace it with?
First, some advice: It's very tricky troubleshooting anything without even an inexpensive digital multimeter. Even a low-grade one will allow you to effectively troubleshoot. Honestly, there's no guarantee that these caps are the only ones damaged.

A quick search showed me that this particular power supply (based on the label) is Philips part number 2722 171 00584, a.k.a power supply module DPS-279BPA. If you search online, you may be able to find a complete replacement.

Please add the model number to the question. The best way to find out exactly what these are is by a schematic or bill of material, which should be in the service manual for the set.

(That being said, I believe the parts are non-safety high voltage ceramic disc capacitors, which any major electronics distributor should sell. You could try Digi-Key.)

Update: I found a service manual which mentions the power supply in your photo. Connectors CN2 and CN3 bring high voltage from the transformer to the backlights, and the four capacitors appear to bring the HV signal down to several protection circuits including overvoltage protection. You should check the integrity of the backlights before trying to fix these caps, it's possible that one of the lamps is dead which led to all of this damage.