Your grandparents aren't likely to be doing any type of gaming but maybe some 2D card game stuff etc., and since you won't be overclocking it, as you'd want a set it and forget it setup with a grandparent situation,
any of the Dual Core Socket 1155 i3 2100 series below will run circles around what is presently being run.http://www.newegg.com/Product/Productcompare.aspx?Submit=ENE&N=100006519%2050001157%2040000343%20600095610%20600005584&IsNodeId=1&bop=And&CompareItemList=343|19-115-093^19-115-093-TS%2C19-115-092^19-115-092-TS%2C19-115-077^19-115-077-TS
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These will handle the light to medium gaming you mentioned with no problems at all, the 8 gigs of memory with Win7 64bit is perfect choice actually.
If you reuse the Dell case you may need an M-ATX motherboard (You'll have to determine what size M/B the case can take), and replace the Dell HDD to say goodbye to the Dell possible proprietorial crap on it.
You will need a stand alone Win7 installation disk not a system restore type of disk, a system restore type disk is tied to the Dell HDD hidden partition in some cases.
The OP/SYS Dell OEM license is on the case, the perfect situation is a genuine Microsoft Win7 installation disk, that you can use to do a scratch installation and then use the existing license, all you have to tell Microsoft is you had to replace the motherboard, if the online auto activation doesn't work, but more than likely it will.
If that is your case deny the auto activation until your new motherboard drivers have been installed, so your lan drivers are functional, just a few tips to help you! Ryan