That's a tight budget, even for a DIY project.
Have you tried a cabinet refacing company like Carolina Custom Cabinets?
Carolina Cabinets | Charlotte N.C.
A rule of thumb for cabinet refacing is about $100-$130 per 'opening'...
So $2750 would get about 22 'openings'. You probably have more like 12-15 openings in a 10'x10' kitchen, which would possibly leave you with about $850-$900 for new counters...