I'm not crazy about Bestec power supplies, but you should have plenty of capacity for a Radeon HD4870. It's the total +12V capacity that matters.
You should notice a significant improvement in your gaming experience when you upgrade from the Radeon X1650.
i7-2600K, H70, P8P67-M Pro, 16 GiB, HD7950, SSD, 3 HD, Blu-ray, X-Fi Ti Pro, Antec P182, S75CF, 3007WFP+2001FP, RK-9000BR, MX518
i5-3570K, GeminII-S524, P8Z77-M Pro, 16 GiB, HD7770, SSD, 2 HD, Blu-ray, InifiniTV4, NSK2480, 55" TV; Asus UX32VD