You'll have to replace all of those other china parts with OEM Honda parts before you'll get it fixed. There is no sense in working on it anymore until you do. We can't help ya get china parts working cause we know from years of experience that china parts are non-functional garbage. Sorry for the rant, I just can't stress that point enough. Your bike won't ever run with those parts on there. In fact other expensive parts can/will get fried with those china parts plugged in!
Now lets get going on solving those china problems... you can look up part numbers here:
But first make darn sure that your bike is a 1987 TRX350D and not a TRX350. The year and model must be correct because the 87 350D is a one-of-kind machine. Ignition & electrical parts from other years and models do not interchange with the 87 350D.
The coil for an 87 350D is #5 on the parts fiche:
Fuel pump is #5 here:
The ignition switch is #4 here:
That Ign switch is discontinued so you'll have to scrounge for either an NOS Honda switch or a used one. Remember, aftermarket do not work, OEM Honda only. AND the OEM switch that you buy MUST match the part number exactly. Other year/model switches do not fit that bike. And most folks don't know that.
Right now you are at a very high risk for frying other components (CDI is next likely candidate to burn if it hasn't already!) on the bike due to those china parts being on there. Disconnect the battery cables immediately and don't connect them back up until every china part has been replaced with OEM parts having the correct part numbers for your year/model.
If there are any wiring harness cobbles or splices then thats suspect too. So look those harnesses over carefully. Replace if someone has "worked" on any of them.
Keep us posted... I imagine the only thing wrong with your bike is someone put china parts on it.