Well, let's see if I can help you out.
I'll piece together a system fron <A HREF="http://www.newegg.com" target="_new">Newegg</A>, my favorite place to shop. By what you said you want an AMD system, so I will make one as such. If you want Intel options, I can oblige. Since it's your mom, I'll try to get her something nice and cheap, instead of coming as close to the $1,000 as possible.
Abit KT7a-RAID - $114+5
AMD AthlonXP 1600+ - $144+7
Inwin case w/ 300w PSU - $56+16 (your mom will like the looks)
2x 128meg Crucial SDRAM - ~$40+0 (check their site for current price)
IBM 60GXP 40GB - $96+9
Visiontek GeForce 2 GTS - $65+5
Hercules Muse XL - $16+9
Pioneer 106s 16x DVD-ROM - $70+10
Teac 24x10x40 - $110+5
Harmon-Kardon HK 19.5 - $29+6
Add that up... grand total of $812, leaving you $198 for monitor/keyboard&mouse/NIC/whatever. I went a bit higher-end for some stuff than I planned, but it came out ok. I can recommend all the components.
This system should look great to her (24x CD-RW, DVD-ROM, etc), but it will actually play games decently well, too.
<font color=orange>Quarter</font color=orange> <font color=blue>Pounder</font color=blue> <font color=orange>Inside</font color=orange>