Tell us more about the wood and the blade you tried. What kind of wood are you cutting, and which blade are you using? Width? TPI?
The thicker the wood, the fewer teeth per inch (TPI) you will want for your blade. If you have high TPI, the motor must work harder because there are more teeth inside the wood trying to cut it. More teeth also means smaller gullets that fill up quickly at the top of the wood and stop cutting the rest of the way through it. More friction means more burning and less cutting. A hot blade dulls quickly.
I would try a new 1/4 inch 3 TPI blade. Tune up the saw as best as you can. Whatever thickness that blade can cut is the best your saw can do. Try it on a scrap of the wood you need to cut. See if it will work for you. While you are at it, inspect the wood to see the blade mark cleanup that you must do afterwards.
You may find that your bandsaw may be able to cut thick basswood (very soft), but not thick maple or cherry. There is a point where the bandsaw simply cannot cut the wood. If you push too hard, the motor cannot power through it. If you push gently and slowly, the blade will overheat, burn the wood, and stop cutting.
If you are new to bandsaws, be sure you learn and follow good bandsaw safety practices. The "bandsaw mentor" in our club once came over to help inspect and setup a new-to-me bandsaw. While he was here, he reminded me that bandsaws were invented for the meat cutting industry. He believes that bandsaws are always trying to "get back to their roots" and have a taste of fresh meat ... so be careful.