ABS module failure does not effect the acceleration. It sounds to me like you have the PNP switch problem. This shows up as flashing ABS and TRACS lights, and causes the transmission to go into the winter mode where it starts out in third gear. A very common issue, and you will find lots or threads under PNP. One short term fix that often works - Park car, turn key on (position II) but don't start motor. Then, put foot on brake and hold there, while you row shifter back and forth from Park to L -back and forth for a whole bunch of times say 20-30 times. Then turn key off, then restart and see if teh lights have gone off. What happens with teh PNP is a combination of corrosion on teh internal switch contacts that control transmission, and the old grease inside teh switch getting hard and keeping teh contacts from easily touching each other. The "rowing" may help for a while, but if it helps at all, it is a sure sign of the need for a PNP in future. Some shops do this rowing routinely on every car they service.
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Mike Sullivan '07 XC70, '95 855T (100k), '95 855 NA (148k). Past Volvo's: '85 744 (256k), '86 245 (165k), '86 245 (195k), '88 745 (208k), '91 745 (196k), '93 965 (147k) , '98 V70XC (98k).