What could be wrong with a 1995 transmission if it shift 1st and 2nd gear but will not shift into 3rd or overdrive?

Ok, First, 95 what? -- Had 92 Honda Accord LX with a burnt R41 Resistor in the A/T Control unit... Located in the floor - under passenger glove box... A/T Box is the one on the right... the other is ECU -- OR.... possibly a vacuum sensor. Do you have any SHIFT indicators sticking when in L2 L1???? IE D or OD light on - while shifter is actually in L1 - L2? Fun stuff.. No kidding about the resistor... A/T CU new -$666. Resistor $2.19.

Have Fun.