Welcome to the forum!

It sounds like the transformer is bad. Try another transformer if you have one. If you have a Lionel dealer in your area, bring it to them and let them check it out.

The train slowing down on the far side of the layout is a classic example of dirty track and/or poor connections between track sections. Take the tracks apart and clean the rails with a ScotchBrite pad to get off any dirt, then wipe them down with a rag dipped in Naphtha until they are clean. Next, polish the pins in the end of the tracks with the ScotchBrite pad. Make sure the pins are a tight fit in the track; crimp the ends of the rails with a needle-nose pliers if necessary.

If you have a large layout, you may need to add extra power wires from the transformer to the far side of the layout to compensate for any voltage drop through the rails.

Larry