G’day CRYSLYNN, the white smoke from your 2012 is probably burned oil. The clanking noise is not good. Have you still got the 2012 bike? Is the oil all black? Burning oil suggests the rings are gone. New pistons with rings & new cylinders may stop the oil being burned. As for the clanking & not firing, i’m guessing there’s something more serious going on. It may be worth taking off the head & cleaning up the valves & checking them out. I would check if the enginge turns MANUALLY. Unscrew the Outer Stator Cover PLUG, put a socket in the hole & turn it Anti-Clockwise (in Neutral gear). If you can’t get the Plug off, you can ROCK the bike gently while IN-GEAR to move the pistons up & down. If the engine is siezed, the BACK WHEEL will LOCK. If the engine turns, the back wheel will move forward a little bit, every time you push it. Don’t force it, just rock the bike forward bit by bit. Hopefully it’s not siezed. Either way, you may be able to repair it. Bikes are generally easier than cars as the parts aren’t heavy. The only pain is the lack of room to get your hands in.
The 2007 sounds ok. I prefer carbys – the EFI bikes seem to be temperamental. You can buy an aftermarket Fuel Cap, Ignition Barrel & Rear Seat Lock, which will come wiht 2x new keys. Removing the ignition barrel is the hardest bit. There’s a special screw (on 1 side i think) that you will need to DRILL OUT probably. I was going to do it but too many other jobs to do first. The FUEL CAP will have to be UNLOCKED before you can REPLACE it with a nice new one. You may need to call a LOCKSMITH out to OPEN that Fuel Cap. Once opened you can undo 3x screws under the lid & pull the whole thing out. He may even MAKE a KEY for YOUR EXISTING Fuel Cap LOCK, so you can keep you iginition barrel & original keys. The aftermarket keys are not identical to hyosung keys (look & feel worse). If the handlebar IGNITION SWITCH is toast & missing wires, take it off. You can get aftermarket or Hyosung switch sets or try a wrecker for a good part. If they wrecked the harness you may get one from a wrecker or Hyosung too. Note: the bike WON’T start in gear & may not start with the STAND DOWN. It won’t tick over. You can cut the wire responsible for this if it annoys you like it does me. Green wire on the CDI box, i think.
If the 2007 bike ticks over a bit, i would try to ROLL-START it. Push the bike with ignition ON, pull in the clutch, drop it into 2nd gear then release the clutch, give it some revs. Sometimes you have to drop it into 1st gear but 2nd is nicer on the bike. If you still have both bikes you are in good shape. You can swap many of the parts to make a good bike. I hope you can fix them both. If you’ve worked on cars you should have no worries replacing pistons, rings & cylinders on the 250. They are tiny pistons & nothing too complicated. The hardest bit is lifting the head off & trying to keep tension on the Cam Chain. If you get someone to hold the chain it’s easy. I popped the camchain back on with a magnet when mine slipped off. Have a look at the VALVES for any damage also, when you take the head off. If you want tips on the process, ive just done it & am about do it again. You can fix that 2007 GT & i reckon with some cash, you can fix that 2012 too. The more Hyosungs out there the better, i reckon. 😆
GT250 Head minus 2x cams & the cam chain:

New Piston, Piston Rings & Gasket into Honed Old Cylinder:

If bike burns oil, your pistons may look like this. Toast … burned toast. Due to deep scratches on the CYLINDER WALLS, from piston contact. Old Oil Seals around the VALVES can also cause oil to be burned in the combustion chamber:

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