I have a 2005 PGO T-Rex 50 but I can't find where the solenoid is and I can't find where to buy a new speedometer.

http://www.crservice.dk/PGO%20mc/Service%20manual/Service%20Manual%20T-Rex%20125_150-v1.pdf

http://www.crservice.dk/PGO%20mc/Service%20manual/Service%20Manual%20T-Rex%20125_150-v1.pdf

An engine, in order to start, needs a good cranking speed, good compression, the right amount of fuel inside the cylinder at the right time and a good spark at the right time.
An engine that doesn't start has one of those things missing and it is pointless guessing which.

The spark plug is probably the easiest to check to begin but it is folly to replace it without checking the spark as part of the process.

motors need three things to run. Fuel, Oxygen, and Ignition (spark).
If you leave motorcycles set for a long time, the gas in the carburetor will turn to lacquer. If that is the case no fuel will get to the spark plug. Spraying starting fluid in the air cleaner or carb can prove this, and it will start and run for a couple seconds then die.
If you can smell gas, you have either no spark or it may be flooded. If you don't have spark, find out if there is a blown fuse, or a shorted wire.

The clock runs of a 186 button battery. remove your mirrors, take out the three phillips head screws under the front of the handle bar cover. Push back on the instrument cluster , theres some small tabs holding it and the lower handle bar cover together. Unscrew your speedo cable and unclip the loom plug to the instrument cluster. Looking at the back of your clock there is a small round cover with a flat slot in it (possibly under a piece of black tape) use a flat head screwdriver to unscrew that a 1/4 turn. There is your battery

Sorry, unable to help. You likely need a service manual. Or ask at a service department and maybe you will get an answer there. Even if it is in the form of a service quote, they would have to tell you what they would need to fix in order to give you a quote.

It is in the middle of the cylinder head.