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First off, welcome to Allpar!
There are a couple of things that could be causing this. Firstly, the A413 (3-speed) is not nearly as picky as the A604 (4-speed) about its fluid, but ATF+4 is recommended. The A413 uses bands to effect gear changes. If you didn't adjust the bands, particularly the kickdown band, this could be causing your problem. Throttle pressure linkage is also suspect, especially if your 1-2 shift seems to have crept up. See http://www.allpar.com/mopar/transmissions/torqueflite-tom-hand.html for more information (an A413 is essentially a down-rated A904 turned sideways). Low fluid level or a clogged valve body could also be at play here. An FSM should have pressure specs and test procedure for diagnosis using the nipples (pressure taps) on the front (well, side, technically, but front if you're looking at it installed) of the transmission case. You'll need a pressure gauge that can read whatever range the tests say, probably up to 250 PSI, and a source of compressed air for the tests, IIRC.
As you'll notice in the block diagrams toward the bottom of that article, the difference between 2 and 3 is the engagement of the front clutch. This may also be the problem, but I imagine a blown front clutch or broken servos would cause no third gear at all (once the band releases, the engine would rev way out, because no gear would be engaged). If adjusting the bands and linkages doesn't fix the problem, and if the tests in the FSM seem to indicate three's an internal problem, you may have to go down the rebuild route. I would not say that it's out of the relam of a DIY'er who has alternate transportation, so long as you have an FSM. It'll be about $150 for a rebuild kit with new steels plus about a week of labor if you take your time. The A413 is a solid, reliable transmission which I would say is worth the rebuild if you think you can handle it. It's essentially the same in concept as any other automatic transmission up through the early 1990's. (As a sidenote, the 4 speed A604 was one of the first electronically controlled transmissions to make it to market, in 1989. It has no bands; all of its gear changes are clutched. As a rule, A604 repairs tend to be more in-depth and expensive. Despite its early problems from teething and improper fluid, the A604, later renamed the 41TE, became the cornerstone of Chrysler's FWD transmission lineup until fairly recently. Its reputation precedes it in may cases, but the 41TE and later A604 are very reliable.)
There are a couple of things that could be causing this. Firstly, the A413 (3-speed) is not nearly as picky as the A604 (4-speed) about its fluid, but ATF+4 is recommended. The A413 uses bands to effect gear changes. If you didn't adjust the bands, particularly the kickdown band, this could be causing your problem. Throttle pressure linkage is also suspect, especially if your 1-2 shift seems to have crept up. See http://www.allpar.com/mopar/transmissions/torqueflite-tom-hand.html for more information (an A413 is essentially a down-rated A904 turned sideways). Low fluid level or a clogged valve body could also be at play here. An FSM should have pressure specs and test procedure for diagnosis using the nipples (pressure taps) on the front (well, side, technically, but front if you're looking at it installed) of the transmission case. You'll need a pressure gauge that can read whatever range the tests say, probably up to 250 PSI, and a source of compressed air for the tests, IIRC.
As you'll notice in the block diagrams toward the bottom of that article, the difference between 2 and 3 is the engagement of the front clutch. This may also be the problem, but I imagine a blown front clutch or broken servos would cause no third gear at all (once the band releases, the engine would rev way out, because no gear would be engaged). If adjusting the bands and linkages doesn't fix the problem, and if the tests in the FSM seem to indicate three's an internal problem, you may have to go down the rebuild route. I would not say that it's out of the relam of a DIY'er who has alternate transportation, so long as you have an FSM. It'll be about $150 for a rebuild kit with new steels plus about a week of labor if you take your time. The A413 is a solid, reliable transmission which I would say is worth the rebuild if you think you can handle it. It's essentially the same in concept as any other automatic transmission up through the early 1990's. (As a sidenote, the 4 speed A604 was one of the first electronically controlled transmissions to make it to market, in 1989. It has no bands; all of its gear changes are clutched. As a rule, A604 repairs tend to be more in-depth and expensive. Despite its early problems from teething and improper fluid, the A604, later renamed the 41TE, became the cornerstone of Chrysler's FWD transmission lineup until fairly recently. Its reputation precedes it in may cases, but the 41TE and later A604 are very reliable.)
