hi mate
yes,anyone who understands how graphic cards work will know that a card like the geforce 8600gt requires a minimum of a 350watt power supply
however its not just about the wattage,you also need a decent amount of amps on the 12 volt dc rail,and in the case of the geforce 8600gt a minimum of 20A on the 12v rail should be fine
a good power supply that meets these requirements is the Xilence 420W Gaming PSU(http://www.aria.co.uk/Products/Components/Power+Supplies/200w+to+449w/Xilence+420W+Gaming+PSU+?productId=19868),this has a 420watt peak output and has dual 12v rails with a total of 27A ,this is more than enough for the geforce 8600gt
it also comes with 2 x sata connectors and a 6 pin pci-express connector,so this fits the bill quite nicely
i recently bought my wife a "acer t671" desktop pc and i was suprised to see it only came with a 250watt psu,however since she is happy to use the xpress 1250 onboard gpu then theres no need to upgrade it
finally you should also look at the cooling in the case aswell,however if its anything like the acer t671 it will have a funnel type cpu cooler and a 80mm rear case fan,these should be fine
your memory is also not compatible,the acer Aspire M1610 can only use DDR2 PC2-5300,DDR2 PC2-4200 with a maximum of 2GB per slot,so you need to get in touch with the retailer were you bought them and see if you can exchange them for the correct modules
so in reflection you need to initially replace the memory and then upgrade the psu and this will sort the crashes out and get you up and running again
you can see the crucial memory report at http://www.crucial.com/store/listparts.aspx?model=Aspire%20M1610
any problems let me know
good luck mate !