I have a lot of talents.

Literal

I [as for-には] many talent [subject-が] exist.

才能がある ('to have talent') is the standard 'have [abstract quality]' pattern — the quality is the grammatical subject of ある. 多くの ('many') modifies 才能 prenominally (via の). 多い alone means 'many' as a predicate; 多くの is the attributive form for modifying a noun.