Well within your budget could you get this,
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Core i5-4690 3.5GHz Quad-Core Processor (£177.92 @ Amazon UK)
Motherboard: ASRock H97M PRO4 Micro ATX LGA1150 Motherboard (£69.91 @ More Computers)
Total: £247.83
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-12-15 15:16 GMT+0000
Plenty of power for the future.
You might have to reinstall windows,but trying and seeing if the current install will start is the only way to know for sure.If it starts would activating it again be enough. With old AMD drivers might it be best though to reinstall no matter what,but that's up to you.
If it doesn't restart do you have to reinstall anyway so make sure you have back-ups of what you want to keep.
I don't know what optiplex you we're looking at so can't say if these parts will work better.I would suggest to just keep on playing with the gtx 550 ti and be happy with it untill there are funds enough to go for better.