Kitchen Large Electric Appliances - Kenmore dryer not drying clothes

Dryer is approx. 13 yrs old & is used alot. Wife tells me that the first load she does seems to dry the clothes as normal but if she tries to do another right after it progressively gets worse & the clothes take as long as 2 hours to dry. The lint screen is on the top & is cleaned every time. The dyer is on breakers & I have checked to see if they are partially tripped & they are not. I have not checked to see if I have 240 at the plug but if the first load is drying ok I am thinking that power is ok. There was a bit of lint caught up in the vent pipe but not real bad. I cleaned it out & dryer is no better. Have not had the back panel off yet.

Looking for suggestions on things to check & if testing is required how to test stuff. I have limited knowledge on electrical. I do have a multi meter but honestly don't understand how to use it that well but sure I could learn with a bit of guidance.

i was about to log off and i read your post. im no expert but i can give you a few suggestions till the smart guys respond. i would unplug the pig tail and make sure all terminals are tight where it connects to the dryer. i would then check the vent pipe on the outside of your home and be sure that the gate ,flapper what ever you want to call it is opening all the way.if its not letting the full volume of air exhaust your dryer will not dry properly.i also have been told that the older the heating element is ,the less efficient it is. hope some of this helps

feel the air flow out of back of dryer,
Than go outside and see if it's the same if not your problem is in the vent. Most dryer problems start there.