Remove rows from dataframe that contains only 0 or just a single 0

Using data.table (assuming df is your data set)

library(data.table)
setDT(df)[, .SD[!all(.SD[, -1, with = F] == 0)], by = GeneName]

#    GeneName ID DU145small DU145total  PC3small  PC3total
# 1:  MIR22HG  1  33221.500   1224.550  2156.430   573.315
# 2: MIRLET7E  2  87566.100   7737.990 25039.300 16415.600
# 3:   MIR612  3      0.000      0.000   530.068     0.000
# 4: MIR218-1  4      0.000      0.000  1166.880   701.253
# 5: MIR181B2  5  70723.200   3958.010  6209.850  1399.340
# 6:   MIR10B  7    787.516    330.556     0.000 20336.400

Or if you only want to remove rows with any zeroes

setDT(df)[, .SD[!any(.SD[, -1, with = F] == 0)], by = GeneName]

#    GeneName ID DU145small DU145total PC3small  PC3total
# 1:  MIR22HG  1    33221.5    1224.55  2156.43   573.315
# 2: MIRLET7E  2    87566.1    7737.99 25039.30 16415.600
# 3: MIR181B2  5    70723.2    3958.01  6209.85  1399.340

Remove rows with any zero:

df[!rowSums(df[-c(1:2)] == 0) >= 1,]

Remove rows with all zeros:

df[!!rowSums(abs(df[-c(1:2)])),]

Inspired by this question

Using rowSums over subset of columns, try this:

#dummy data
df <- read.table(text="
ID  GeneName    DU145small  DU145total  PC3small    PC3total
1   MIR22HG     33221.5     1224.55     2156.43     573.315
2   MIRLET7E    87566.1     7737.99     25039.3     16415.6
3   MIR612      0           0           530.068     0
4   MIR218-1    0           0           1166.88     701.253
5   MIR181B2    70723.2     3958.01     6209.85     1399.34
6   MIR218-2    0           0           0           0
7   MIR10B      787.516     330.556     0           20336.4
8   MIR3176     0           0           0           0",
                 header=TRUE)
#remove any zero
df[ !rowSums(df[,colnames(df)[(3:ncol(df))]]==0)>=1, ]

#remove all zero
df[ !rowSums(df[,colnames(df)[(3:ncol(df))]]==0)==ncol(df)-2, ]