Pina's solution for your problem, given that P1 is scorched, is to re-solder c15, p1, & L2. If that does not fix the problem replace C15, preferably with a 3.9 mfd NP HF 100 V 85 〬C , L2 may also have to be replaced. If the plating is burned off pin 4 of P1, you'll have to replace the connector. Once you re-flow the solder on everything (before replacing anything), try slapping the case on the side and see if your horizontal sweep snaps on. That's a good sign only the connector needs to be replaced. If the L2 is not fused (i.e. can't be removed), it should be OK. Possibly true for L3. But if all that doesn't change anything, start looking to replace C15, which is extremely hard to test accurately in-circuit. Also, Pina recommends that if a re-flow fails and you have a known good C15, L2 & L3, then you should vacuum de-solder all components and re-solder with fresh new solder.

Ain't this fun!