According to www.game-dabate.com the recommended system requirements and your actual system do not differ much except for the RAM memory.
Similarly, the official minimum system requirements state:
- OS: Windows® XP SP 3 (32-64 bits) -- CHECK
- Processor: Intel Core® 2 Duo 1.8 GHZ or AMD Athlon X2 64 2.4GHZ -- CHECK
- Memory: 1.5 GB Windows® XP / 2 GB Windows Vista® - Windows 7® -- YOU NEED MORE RAM!
- Graphics: 256 MB DirectX® 9.0 compliant card with Shader Model 3.0 or higher (see supported list) -- NVIDIA GeForce ® 7 (7600 or better)/8/9/100/200 series. -- Even though the 6xxx series are not listed there, your GPU supports D.X 9 and Shader 3.0 :) -- CHECK
Source: NFS minimum system specs
Conclusion: You will most likely be able to play with all settings at minimum, however by improving RAM, and I would highly recommend you to do so (2x1GB DDR2 - 25-30USD max!) you will be able to enjoy NFS HP even in medium settings!!