It's always worth a look at, post the specs...can't say much without actual makes and models in there.
As for your original system, no problems there, depending on what you're using it for. I still run WC3, CS:S and WOW on my athlon 3000+ laptop and athlon 2800+ desktop with a 7300GT AGP in it...super dated but they are both primary work computers for word, excel, power point and do just fine for those causes and the BASIC gaming, haven't tried CRYSIS on them yet
ha!
If you're looking to pinch pennies on your build and are determined to go AMD here are a few changes that could save you a bit, this is a pretty standard list for a budget AMD game build:
CPU $60.00:
Newegg.com - AMD Athlon 64 X2 4000+ Brisbane 2.1GHz 2 x 512KB L2 Cache Socket AM2 65W Dual-Core Processor - Retail
Cooler $20.00:
Newegg.com - ARCTIC COOLING Freezer 64 Pro 92mm CPU Cooler - Retail
RAM $40.00:
Newegg.com - Crucial Ballistix 2GB (2 x 1GB) 240-Pin DDR2 SDRAM DDR2 800 (PC2 6400) Dual Channel Kit Desktop Memory - Retail
The X2 4000+ with that cooler should hit 3.0 without much problem, my brother runs his at 2.8 on the stock cooler. my 3600+ runs at 3.0 with the AC 64 mentioned. The ballistix is better than the OCZ RAM, I had problems with my OCZ platinums and returned them for Ballistix, i have 4GB of it running in two different systems, no problems at all and OC very well.