I don't know the specifics of your sewing machine, but a couple good things to check on any sewing machine. Is the foot up? If it isn't, there should be a lever to raise it up. Is the needle out of the work? If not, there's a knob on the machine that moves the needle by hand. It's usually on the right hand side of the machine. Hope one of these helps you.

When you're desoldering something that small, sometimes desoldering braid alone isn't enough. The 'best' way to do it is with a hot air rework station, so you can heat up the entire part at once the pull it off with tweezers. The problem with that is that those are expensive. The next best way to do it is to use desoldering braid to remove most of the solder, then heat up one of the pads, and while it's hot, gently slide something like an exacto knife under the part to separate it from the board. Do this with all the pads and the part should come off. The big trick is to be gentle. If it doesn't work right the first time, just put a little bit of solder back onto the part and use the desoldering braid again.

It sounds like you don't have the right input selected on your TV. Since I don't know the model, I can't give you exact instructions, but there should be a button marked input on either the TV itself, or on the remote. Turn the Nintendo64 on, then press the input button until the picture shows up on the screen. Hope this helps