Now given the fact that your PSU is a 650w unit.
Now eXtreme Power Supply Calculator Lite
states that your rig should draw 401w at the most.
Things you need to look into are :-
1) Power factor of your UPS of interest. For example one that is rated 650va and 390w has a power factor of 390 / 650 = 0.61
The higher the power factor the better the UPS. Most UPS out there are rated by their VA not so much the W which means a tonne when it
comes to the right UPS for your rig.
2) How long you plan on having your PC draw such a high wattage (400w) from the UPS. Given that your UPS is instantly shutting off, this means your system is drawing more than it can handle and to it, it sees it a short circuit and shuts off immediately.
3) Pure sine wave vs modified sine wave UPS. Now the pure sine wave is the best and also the most expensive vs the modified. PC applications do not need pure sine wave since the wave has to undergo rectification into a DC meaning the modified sive wave UPS will be good enough for your PC.
To help you even further, I have given you an option below which would be quite good for your PC given that you are on a budget and don't have much money to spend on a UPS:-
It has an impressive power factor of 0.67 which greatly impacts on your power bills and especially the longevity of your backup batteries. It has a backup runtime of 14-15min at power draw 400w allowing you to game just that long before it shuts off. If you feel money is no object and want to run more than an hour at 400w (gaming power) check this out:-
It has an utterly impressive power factor of 0.9
meaning batteries even get to last much much longer due to high efficiency both at online and offline mode.
Alternatively you can be like me (Industrial electronics backgrounded). I took a Russian UPS studied its behavior for 3 years, understood its operating parameters and currently have it run for upto 8 hrs a day up from a bare maximum of 10min on my system. The unit has a very poor power factor of 0.5 as it is a 600va, 300w unit but soon to be replaced with one of the mentioned above and add some compensation circuitry to avoid working outside its normal parameters in order to sustain an 8 hr non stop run. To modify an existing UPS, I must understand it inside out by how it is wired then I can pull any stunt I want with it.