It's a difficult one. The GX620 has a Pentium 4, which was a lousy processor when it was released 13 years ago and is now positively antique. Similarly, onboard graphics of the time were also pretty poor, hence I'm not to surprised that support is being dropped for a system which went out of production 8 years ago. An upgrade is possible, but probably not worth the money.
The system you're looking at is a big step forwards, depends when you can afford it. Another option would be to scour eBay in the meantime. You might find a discrete graphics card that will do for £10-£15 or so. Might keep you ticking over until you can afford the replacement PC.
I wouldn't spend too much on your current PC though as its age means it just isn't worth it.
EDITED: 1 Mar 2014 00:07 by DAVE!!