There are a lot of used and refurbished cars around on sale. I'm afraid only, the sellers do not speak English well and seeing you're a foreigner, would offer you much higher rates.
If you need a car just temporarily, you could buy one of those used garbage of course... for about 2-3-4 thousands EURos, depends on the model and production year... anyway, nobody will give you warranties on that car.
I think you may visit a place called "Rumbula", it's on the border of Riga if you drive to the Eastern Latvia. There you may find huge amount of second-hand cars.
Regarding new cars... yes, in Latvia now there is a financial crisis, and many banks are selling quite new cars instead of receiving the loan's fee, for quite moderate prices. But I guess such chance won't live for a long time